Duality Theorems for the Homology of Manifolds
An n-dimensional manifold is a Hausdorff space such that every point has an open neighborhood which is homeomorphic to Euclidean n-space, R n (see Massey, , Chapter I). One of the main goals of this chapter will be to prove one of the oldest results of algebraic topology, the famous Poincaré duality theorem for compact, orientable manifolds. It is easy to state the Poincaré duality theorem but the proof is lengthy.
KeywordsHomology Group Direct Limit Duality Theorem Homology Class Cohomology Theory
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Bibliography for Chapter IX
- H. Cartan, Seminaire Henri Cartan 1948/49: Topologie Algébrique, W. A. Ben-jamin, Inc., New York, 1967.Google Scholar
- W. S. Massey, Algebraic Topology: An Introduction, Springer-Verlag, New York, 1978.Google Scholar
- J. Milnor, Lectures on Characteristic Classes, Princeton University Press, Princeton, 1974.Google Scholar