D.B. Fuks's Books

Beginner's Course In Topology

Geometric Chapters

By: D. B. Fuks,V. A. Rokhlin

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Beginner's Course In Topology

Geometric Chapters

By: D. B. Fuks,V. A. Rokhlin

This book is the result of reworking part of a rather lengthy course of lectures of which we delivered several versions at the Leningrad and Moscow Universities. In these lectures we presented an introduction to the fundamental topics of topology: homology theory, homotopy theory, theory of bundles, and topology of manifolds. The structure of the course was well determined by the guiding term elementary topology, whose main significance resides in the fact that it made us use a rather simple apparatus. tn this book we have retained {hose sections of the course where algebra plays a subordinate role. We plan to publish the more algebraic part of the lectures as a separate book. Reprocessing the lectures to produce the book resulted in the profits and losses inherent in such a situation: the rigour has increased to the detriment of the intuitiveness, the geometric descriptions have been replaced by formulas needing interpretations, etc. Nevertheless, it seems to us tha·t the book retains the main qualities of our lectures: their elementary, systematic, and pedagogical features. The preparation of the reader is assumed to be limi ted to the usual knowledge of set ·theory, algebra, and calculus which mathematics students should master after the first year and a half of studies. The exposition is accompanied by examples and exercises. We hope that the book can be used as a topology textbook.

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536

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540135774

ISBN 13

9783540135777

Mathematical Omnibus

Thirty Lectures on Classic Mathematics

By: D. B. Fuks,Serge Tabachnikov

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Mathematical Omnibus

Thirty Lectures on Classic Mathematics

By: D. B. Fuks,Serge Tabachnikov

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 solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

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Page Count

482

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843168

ISBN 13

9780821843161

Cohomology of Infinite-Dimensional Lie Algebras

By: D.B. Fuks

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Cohomology of Infinite-Dimensional Lie Algebras

By: D.B. Fuks

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 infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional 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 infinite-dimensional 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.

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347

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468487655

ISBN 13

9781468487657

Topology II

Homotopy and Homology. Classical Manifolds

By: D.B. Fuchs,O.Ya. Viro

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Topology II

Homotopy and Homology. Classical Manifolds

By: D.B. Fuchs,O.Ya. Viro

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

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Page Count

264

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662105810

ISBN 13

9783662105818

Cohomology of Infinite-Dimensional Lie Algebras

By: D.B. Fuks

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Cohomology of Infinite-Dimensional Lie Algebras

By: D.B. Fuks

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Page Count

347

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Springer Science & Business Media

Published Date

ISBN 10

1468487655

ISBN 13

9781468487657

Beginner's Course In Topology

Geometric Chapters

By: D. B. Fuks,V. A. Rokhlin

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Beginner's Course In Topology

Geometric Chapters

By: D. B. Fuks,V. A. Rokhlin

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N/A

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Solve jigsaw puzzle

Age

Page Count

536

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540135774

ISBN 13

9783540135777

Book's by D.B. Fuks

Beginner's Course In Topology

Beginner's Course In Topology

Mathematical Omnibus

Mathematical Omnibus

Cohomology of Infinite-Dimensional Lie Algebras

Cohomology of Infinite-Dimensional Lie Algebras

Topology II

Topology II

Cohomology of Infinite-Dimensional Lie Algebras

Cohomology of Infinite-Dimensional Lie Algebras

Beginner's Course In Topology

Beginner's Course In Topology

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