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Introduction to Topology
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Librairie Eyrolles - Paris 5e
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Introduction to Topology

Introduction to Topology

V.A. Vassiliev

148 pages, parution le 17/12/2001

Résumé

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, homology and cohomology, 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."

Contents

  • Topological spaces and operations with them
  • Homotopy groups and homotopy equivalence
  • Coverings
  • Cell spaces ($CW$-complexes)
  • Relative homotopy groups and the exact sequence of a pair
  • Fiber bundles
  • Smooth manifolds
  • The degree of a map
  • Homology: Basic definitions and examples
  • Main properties of singular homology groups and their computation
  • Homology of cell spaces
  • Morse theory
  • Cohomology and Poincaré duality
  • Some applications of homology theory
  • Multiplication in cohomology (and homology)
  • Index of notations
  • Subject index

Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) V.A. Vassiliev
Parution 17/12/2001
Nb. de pages 148
Format 14 x 21,5
Couverture Broché
Poids 200g
Intérieur Noir et Blanc
EAN13 9780821821626
ISBN13 978-0-8218-2162-6

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