Intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory.
Contents: * Two-Dimensional Manifolds * The Fundamental Group * Free Groups and Free Products of Groups * Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications * Covering Spaces * Background and Motivation for Homology Theory * Definitions and Basic Properties of Homology Theory * Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory * Homology of CW-Complexes * Homology with Arbitrary Coefficient Groups * The Homology of Product Spaces * Cohomology Theory * Products in Homology and Cohomology * Duality Theorems for the Homology in Manifolds * Cup Products in Projective Spaces and Applications of Cup Products * A Proof of De Rham's Theorem * Permutation Groups or Transformation Groups
1991/428 PP., 57 ILLUS./HARDCOVER/$54.95/ISBN
GRADUATE TEXTS IN MATHEMATICS, VOLUME 127
Copyright ©1997 Springer-Verlag NY. All rights reserved.