Normal view MARC view ISBD view

Hatcher, Allen

Algebraic topology/ Allen Hatcher - Cambridge: Cambridge University Press, 2002. - xii, 544 p. : ill. ; 26 cm.

Some Underlying Geometric Notions --
Homotopy and Homotopy Type --
Cell Complexes --
Operations on Spaces --
Two Criteria for Homotopy Equivalence --
The Homotopy Extension Property --
The Fundamental Group --
Basic Constructions --
Paths and Homotopy --
The Fundamental Group of the Circle --
Induced Homomorphisms --
Van Kampen's Theorem --
Free Products of Groups --
The van Kampen Theorem --
Applications to Cell Complexes --
Covering Spaces --
Lifting Properties --
The Classification of Covering Spaces --
Deck Transformations and Group Actions --
Graphs and Free Groups --
K(G,1) Spaces and Graphs of Groups --
Homology --
Simplicial and Singular Homology --
[Delta]-Complexes --
Simplicial Homology --
Singular Homology --
Homotopy Invariance --
Exact Sequences and Excision --
The Equivalence of Simplicial and Singular Homology --
Computations and Applications --
Degree --
Cellular Homology --
Mayer-Vietoris Sequences --
Homology with Coefficients --
The Formal Viewpoint --
Axioms for Homology --
Categories and Functors --
Homology and Fundamental Group --
Classical Applications --
Simplicial Approximation --
Cohomology --
Cohomology Groups --
The Universal Coefficient Theorem --
Cohomology of Spaces --
Cup Product --
The Cohomology Ring --
A Kunneth Formula --
Spaces with Polynomial Cohomology --
Poincare Duality --
Orientations and Homology --
The Duality Theorem --
Connection with Cup Product --
Other Forms of Duality --
Universal Coefficients for Homology --
The General Kunneth Formula.

ISBN: 9780521795401 9780521541862

Subjects--Topical Terms:
Algebraic topology

Dewey Class. No.: 514.2 / HAT/A