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Introduction to Topology
 
V. A. Vassiliev Independent University of Moscow, Moscow, Russia
Introduction to Topology
Softcover ISBN:  978-0-8218-2162-6
Product Code:  STML/14
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2130-4
Product Code:  STML/14.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-2162-6
eBook: ISBN:  978-1-4704-2130-4
Product Code:  STML/14.B
List Price: $108.00 $83.50
Introduction to Topology
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Introduction to Topology
V. A. Vassiliev Independent University of Moscow, Moscow, Russia
Softcover ISBN:  978-0-8218-2162-6
Product Code:  STML/14
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2130-4
Product Code:  STML/14.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-2162-6
eBook ISBN:  978-1-4704-2130-4
Product Code:  STML/14.B
List Price: $108.00 $83.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 142001; 149 pp
    MSC: 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.”

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 142001; 149 pp
MSC: 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.”

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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