Duality Theorems for the Homology of Manifolds
Part of the
Graduate Texts in Mathematics
book series (GTM, volume 70)
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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© Springer-Verlag New York Inc. 1980