Introduction to Topology

V.A. Vassiliev

148 pages, parution le 17/12/2001

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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