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Duality Theorems for the Homology of Manifolds

  • William S. Massey
Part of the Graduate Texts in Mathematics book series (GTM, volume 70)

Abstract

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, [6], 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.

Keywords

Homology Group Direct Limit Duality Theorem Homology Class Cohomology Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography for Chapter IX

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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • William S. Massey
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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