Softcover ISBN:  9780821821626 
Product Code:  STML/14 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421304 
Product Code:  STML/14.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821821626 
eBook: ISBN:  9781470421304 
Product Code:  STML/14.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9780821821626 
Product Code:  STML/14 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421304 
Product Code:  STML/14.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821821626 
eBook ISBN:  9781470421304 
Product Code:  STML/14.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 14; 2001; 149 ppMSC: Primary 55
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, intersection index, etc. The author notes, “The lecture note origins of the book left a significant imprint on its style. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs.” He concludes, “As a rule, only those proofs (or sketches of proofs) that are interesting per se and have important generalizations are presented.”
ReadershipGraduate students, research mathematicians, and theoretical physicists.

Table of Contents

Chapters

Chapter 1. Topological spaces and operations with them

Chapter 2. Homotopy groups and homotopy equivalence

Chapter 3. Coverings

Chapter 4. Cell spaces ($CW$complexes)

Chapter 5. Relative homotopy groups and the exact sequence of a pair

Chapter 6. Fiber bundles

Chapter 7. Smooth manifolds

Chapter 8. The degree of a map

Chapter 9. Homology: Basic definitions and examples

Chapter 10. Main properties of singular homology groups and their computation

Chapter 11. Homology of cell spaces

Chapter 12. Morse theory

Chapter 13. Cohomology and Poincaré duality

Chapter 14. Some applications of homology theory

Chapter 15. Multiplication in cohomology (and homology)


Additional Material

Reviews

The book will be very convenient for those who want to be acquainted with the topic in a short time.
European Mathematical Society Newsletter 
A concise treatment of differential and algebraic topology.
American Mathematical Monthly 
In little over 140 pages, the book goes all the way from the definition of a topological space to homology and cohomology theory, Morse theory, Poincaré theory, and more ... emphasizes intuitive arguments whenever possible ... a broad survey of the field. It is often useful to have an overall picture of a subject before engaging it in detail. For that, this book would be a good choice.
MAA Online 
From a review of the Russian edition ...
The book is based on a course given by the author in 1996 to first and second year students at Independent Moscow University ... the emphasis is on illustrating what is happening in topology, and the proofs (or their ideas) covered are those which either have important generalizations or are useful in explaining important concepts ... This is an excellent book and one can gain a great deal by reading it. The material, normally requiring several volumes, is covered in 123 pages, allowing the reader to appreciate the interaction between basic concepts of algebraic and differential topology without being buried in minutiae.
Mathematical Reviews


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, intersection index, etc. The author notes, “The lecture note origins of the book left a significant imprint on its style. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs.” He concludes, “As a rule, only those proofs (or sketches of proofs) that are interesting per se and have important generalizations are presented.”
Graduate students, research mathematicians, and theoretical physicists.

Chapters

Chapter 1. Topological spaces and operations with them

Chapter 2. Homotopy groups and homotopy equivalence

Chapter 3. Coverings

Chapter 4. Cell spaces ($CW$complexes)

Chapter 5. Relative homotopy groups and the exact sequence of a pair

Chapter 6. Fiber bundles

Chapter 7. Smooth manifolds

Chapter 8. The degree of a map

Chapter 9. Homology: Basic definitions and examples

Chapter 10. Main properties of singular homology groups and their computation

Chapter 11. Homology of cell spaces

Chapter 12. Morse theory

Chapter 13. Cohomology and Poincaré duality

Chapter 14. Some applications of homology theory

Chapter 15. Multiplication in cohomology (and homology)

The book will be very convenient for those who want to be acquainted with the topic in a short time.
European Mathematical Society Newsletter 
A concise treatment of differential and algebraic topology.
American Mathematical Monthly 
In little over 140 pages, the book goes all the way from the definition of a topological space to homology and cohomology theory, Morse theory, Poincaré theory, and more ... emphasizes intuitive arguments whenever possible ... a broad survey of the field. It is often useful to have an overall picture of a subject before engaging it in detail. For that, this book would be a good choice.
MAA Online 
From a review of the Russian edition ...
The book is based on a course given by the author in 1996 to first and second year students at Independent Moscow University ... the emphasis is on illustrating what is happening in topology, and the proofs (or their ideas) covered are those which either have important generalizations or are useful in explaining important concepts ... This is an excellent book and one can gain a great deal by reading it. The material, normally requiring several volumes, is covered in 123 pages, allowing the reader to appreciate the interaction between basic concepts of algebraic and differential topology without being buried in minutiae.
Mathematical Reviews