Fuks, D. B.
Overview
Works:  54 works in 183 publications in 6 languages and 2,766 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Translator, Honoree 
Publication Timeline
.
Most widely held works by
D. B Fuks
Beginner's course in topology : geometric chapters by
V. A Rokhlin(
Book
)
19 editions published between 1981 and 2004 in English and Undetermined and held by 440 WorldCat member libraries worldwide
19 editions published between 1981 and 2004 in English and Undetermined and held by 440 WorldCat member libraries worldwide
Mathematical omnibus : thirty lectures on classic mathematics by
D. B Fuks(
Book
)
13 editions published between 2007 and 2012 in English and Japanese and held by 359 WorldCat member libraries worldwide
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutio
13 editions published between 2007 and 2012 in English and Japanese and held by 359 WorldCat member libraries worldwide
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutio
Cohomology of infinitedimensional Lie algebras by
D. B Fuks(
Book
)
15 editions published between 1986 and 1998 in English and Spanish and held by 318 WorldCat member libraries worldwide
There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinitedimensional Lie algebras differs markedly from the theory of finitedimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinitedimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study
15 editions published between 1986 and 1998 in English and Spanish and held by 318 WorldCat member libraries worldwide
There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinitedimensional Lie algebras differs markedly from the theory of finitedimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinitedimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study
Homotopical topology by
A. T Fomenko(
)
8 editions published in 2016 in English and Undetermined and held by 310 WorldCat member libraries worldwide
"This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basicsthe fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebrathe book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, Ktheory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topologythe Adams conjecture, Bott periodicity, the HirzebruchRiemannRoch theorem, the AtiyahSinger index theorem, to name a fewpaints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader's mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A.T. Fomenko artistically render the wondrous beauty, and mystery, of the subject" Page 4 of cover
8 editions published in 2016 in English and Undetermined and held by 310 WorldCat member libraries worldwide
"This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basicsthe fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebrathe book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, Ktheory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topologythe Adams conjecture, Bott periodicity, the HirzebruchRiemannRoch theorem, the AtiyahSinger index theorem, to name a fewpaints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader's mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A.T. Fomenko artistically render the wondrous beauty, and mystery, of the subject" Page 4 of cover
Experimental mathematics by
V. I Arnolʹd(
Book
)
2 editions published in 2015 in English and held by 222 WorldCat member libraries worldwide
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the bestknown examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred yeras. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conduting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. page 4 de la couverture
2 editions published in 2015 in English and held by 222 WorldCat member libraries worldwide
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the bestknown examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred yeras. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conduting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. page 4 de la couverture
Differential topology, infinitedimensional lie algebras, and applications : D.B. Fuchs' 60th anniversary collection(
Book
)
3 editions published in 1999 in English and held by 217 WorldCat member libraries worldwide
This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics. The main topics addressed in this unique work are infinitedimensional Lie algebras with applications (vertex operator algebras, conformal field theory, quantum integrable syst
3 editions published in 1999 in English and held by 217 WorldCat member libraries worldwide
This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics. The main topics addressed in this unique work are infinitedimensional Lie algebras with applications (vertex operator algebras, conformal field theory, quantum integrable syst
Ein Schaubild der Mathematik by
D. B Fuks(
)
7 editions published in 2011 in German and held by 179 WorldCat member libraries worldwide
Das Buch enthält dreißig Vorlesungen über unterschiedliche Themen, die einen Großteil der mathematischen Landschaft abdecken, anstatt sich nur auf ein Gebiet zu konzentrieren. Klar und verständlich wird der Leser auf zahlreiche Resultate geführt, die oft weder in der mathematischen Grundausbildung noch im akademischen Curriculum vorkommen. So kann der Leser Zusammenhänge zwischen klassischen und modernen Ideen aus der Algebra, der Kombinatorik, der Geometrie und der Topologie entdecken. Die Bemühungen des Lesers werden durch die Einsicht in die Harmonie jedes Themas belohnt. Die ausgewählten Themen verbindet, dass sie die Einheit und die Schönheit der Mathematik veranschaulichen. Die meisten Vorlesungen enthalten Übungen, ausgewählte Übungen werden am Ende des Buches gelöst oder beantwortet. Zu den Besonderheiten dieses Buches zählen die Fülle von Zeichnungen (es sind über vierhundert), die Illustrationen eines versierten Künstlers sind, und die rund einhundert Porträts von Mathematikern, die sich um die in den einzelnen Vorlesungen behandelten Themen verdient gemacht haben. Fast jede Vorlesung hält auch für den erfahrenen Forscher Überraschungen bereit
7 editions published in 2011 in German and held by 179 WorldCat member libraries worldwide
Das Buch enthält dreißig Vorlesungen über unterschiedliche Themen, die einen Großteil der mathematischen Landschaft abdecken, anstatt sich nur auf ein Gebiet zu konzentrieren. Klar und verständlich wird der Leser auf zahlreiche Resultate geführt, die oft weder in der mathematischen Grundausbildung noch im akademischen Curriculum vorkommen. So kann der Leser Zusammenhänge zwischen klassischen und modernen Ideen aus der Algebra, der Kombinatorik, der Geometrie und der Topologie entdecken. Die Bemühungen des Lesers werden durch die Einsicht in die Harmonie jedes Themas belohnt. Die ausgewählten Themen verbindet, dass sie die Einheit und die Schönheit der Mathematik veranschaulichen. Die meisten Vorlesungen enthalten Übungen, ausgewählte Übungen werden am Ende des Buches gelöst oder beantwortet. Zu den Besonderheiten dieses Buches zählen die Fülle von Zeichnungen (es sind über vierhundert), die Illustrationen eines versierten Künstlers sind, und die rund einhundert Porträts von Mathematikern, die sich um die in den einzelnen Vorlesungen behandelten Themen verdient gemacht haben. Fast jede Vorlesung hält auch für den erfahrenen Forscher Überraschungen bereit
Homotopic topology by
D. B Fuks(
Book
)
8 editions published in 1986 in English and held by 149 WorldCat member libraries worldwide
8 editions published in 1986 in English and held by 149 WorldCat member libraries worldwide
Unconventional Lie algebras by
D. B Fuks(
Book
)
5 editions published in 1993 in English and Undetermined and held by 148 WorldCat member libraries worldwide
This book contains eight papers on representations and cohomology of Lie algebras. The Lie algebras here are either infinitedimensional, are defined over fields of finite characteristic, or are actually Lie superalgebras or quantum groups. Among the topics covered here are generalizations of the Virasoro algebra, representation theory of the Virasoro algebra and of KacMoody algebras, cohomology of Lie algebras of vector fields on the line, and Lie superalgebras of vector fields. The paper by Retakh and Shander contains a generalization of the Schwarz derivative to the noncommutative case
5 editions published in 1993 in English and Undetermined and held by 148 WorldCat member libraries worldwide
This book contains eight papers on representations and cohomology of Lie algebras. The Lie algebras here are either infinitedimensional, are defined over fields of finite characteristic, or are actually Lie superalgebras or quantum groups. Among the topics covered here are generalizations of the Virasoro algebra, representation theory of the Virasoro algebra and of KacMoody algebras, cohomology of Lie algebras of vector fields on the line, and Lie superalgebras of vector fields. The paper by Retakh and Shander contains a generalization of the Schwarz derivative to the noncommutative case
Northern California symplectic geometry seminar(
Book
)
1 edition published in 1999 in English and held by 147 WorldCat member libraries worldwide
This seminar was established to encourage ongoing interaction between geometers at Stanford University and the University of California (Berkeley, Davis, and Santa Cruz). Over the years, lectures presented have provided a panorama of developments in symplectic and contact geometry and topology, Poisson geometry, quantization theory, and applications. This volume includes papers by several of the distinguished seminar participants. The diversity of the topics from the seminar are reflected in the informative presentations. A wide range of topics are presented in the book, including symplectic t
1 edition published in 1999 in English and held by 147 WorldCat member libraries worldwide
This seminar was established to encourage ongoing interaction between geometers at Stanford University and the University of California (Berkeley, Davis, and Santa Cruz). Over the years, lectures presented have provided a panorama of developments in symplectic and contact geometry and topology, Poisson geometry, quantization theory, and applications. This volume includes papers by several of the distinguished seminar participants. The diversity of the topics from the seminar are reflected in the informative presentations. A wide range of topics are presented in the book, including symplectic t
Premier cours de topologie : chapitres geometriques by
V. A Rokhlin(
Book
)
11 editions published in 1981 in French and Undetermined and held by 74 WorldCat member libraries worldwide
11 editions published in 1981 in French and Undetermined and held by 74 WorldCat member libraries worldwide
Kurs gomotopicheskoĭ topologii by
A. T Fomenko(
)
3 editions published in 1989 in Russian and held by 44 WorldCat member libraries worldwide
3 editions published in 1989 in Russian and held by 44 WorldCat member libraries worldwide
Kogomologii beskonechnomernykh algebr Li by
D. B Fuks(
Book
)
2 editions published in 1984 in Russian and held by 21 WorldCat member libraries worldwide
2 editions published in 1984 in Russian and held by 21 WorldCat member libraries worldwide
Gomotopicheskai︠a︡ topologii︠a︡ by
D. B Fuks(
Book
)
8 editions published between 1967 and 1969 in Russian and held by 18 WorldCat member libraries worldwide
8 editions published between 1967 and 1969 in Russian and held by 18 WorldCat member libraries worldwide
Selfdual polygons and selfdual curves(
)
1 edition published in 2007 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 15 WorldCat member libraries worldwide
Topology I : general survey, classical manifolds(
Book
)
2 editions published between 1991 and 1996 in English and held by 11 WorldCat member libraries worldwide
2 editions published between 1991 and 1996 in English and held by 11 WorldCat member libraries worldwide
Gomotopieskaja topologija by
D. B Fuks(
Book
)
9 editions published between 1967 and 1969 in Russian and Undetermined and held by 11 WorldCat member libraries worldwide
9 editions published between 1967 and 1969 in Russian and Undetermined and held by 11 WorldCat member libraries worldwide
Kogomologii beskonečnomernych algebr Li by
D. B Fuks(
Book
)
5 editions published in 1984 in Russian and held by 10 WorldCat member libraries worldwide
5 editions published in 1984 in Russian and held by 10 WorldCat member libraries worldwide
Nachalʹnyĭ kurs topologii : geometricheskie glavy by
V. A Rokhlin(
Book
)
6 editions published between 1977 and 1997 in Russian and Undetermined and held by 10 WorldCat member libraries worldwide
6 editions published between 1977 and 1997 in Russian and Undetermined and held by 10 WorldCat member libraries worldwide
Cohomology of groups by
Kenneth S Brown(
Book
)
2 editions published in 1987 in Russian and held by 4 WorldCat member libraries worldwide
As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics
2 editions published in 1987 in Russian and held by 4 WorldCat member libraries worldwide
As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics
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Related Identities
 Tabachnikov, Serge Editor
 Fomenko, A. T. Author
 Rokhlin, V. A. Author
 Arnolʹd, V. I. (Vladimir Igorevich) 19372010 Author
 Saul, Mark E. Translator
 Astashkevich, Alexander Editor
 Gutenmakher, V. L. (Viktor Lʹvovich)
 Rațiu, Tudor S. Editor
 Weinstein, Alan 1943 Editor
 Eliashberg, Y. 1946 Editor
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Associated Subjects
Algebra Algebra, Homological Algebraic topology Categories (Mathematics) Combinatorial analysis Differential topology Experimental mathematics Functions Geometry Geometry, Algebraic Group theory Homology theory Homotopy theory Infinite dimensional Lie algebras Ktheory Lie algebras Manifolds (Mathematics) Mathematics Soviet Union Symplectic geometry Symplectic groups Topological algebras Topological groups Topology
Covers
Alternative Names
Dmitry Borisovich Fuchs American mathematician
Dmitry Borisovich Fuchs matemático ruso
Dmitry Borisovich Fuchs Russian mathematician
Dmitry Fuchs
Dmitry Fuchs matemàtic rus
Dmitry Fuchs mathématicien russe
Dmitry Fuchs russischUSamerikanischer Mathematiker
Dmitry Fuchs Russisch wiskundige
Fouks, Dmitri Borisovich
Fouks, Dmitri Borisovitch
Fuchs, D.
Fuchs, D. B.
Fuchs, D.B. 1939
Fuchs, Dimitrii Borisivich
Fuchs, Dmitrij 1939
Fuchs, Dmitry.
Fuchs, Dmitry 1939
Fuchs, Dmitry B.
Fuchs, Dmitry B. 1939
Fuchs, Dmitry Borisovich 1939
Fuchs, Mitya
Fuks, D.
Fuks, D.B.
Fuks, D. B. 1939
Fuks, Dimitrij Borisovič
Fuks, Dimitrij Borisovič 1939
Fuks, Dmitriĭ Borisovich
Fuks, Dmitrij B.
Fuks, Dmitrij Borisovič
Fuks, Dmitrij Borisovič 1939...
Fuks, Dmitrij Borisovich
Fuks, Dmitrij Borisovitch
Дмитри Фукс
Фукс, Д 1939
Фукс, Дмитрий Борисович
Фукс, Дмитрий Борисович 1939...
フックス, D.
Languages