Ranicki, Andrew

Singularities, double points, controlled topology and chain duality

Doc. Math., J. DMV 4, 1-59 (1999)

Summary

Summary: A manifold is a Poincaré duality space without singularities. McCrory obtained a homological criterion of a global nature for deciding if a polyhedral Poincaré duality space is a homology manifold, i.e. if the singularities are homologically inessential. A homeomorphism of manifolds is a degree 1 map without double points. In this paper combinatorially controlled topology and chain complex methods are used to provide a homological criterion of a global nature for deciding if a degree 1 map of polyhedral homology manifolds has acyclic point inverses, i.e. if the double points are homologically inessential.

Mathematics Subject Classification

55N45, 57R67, 55U35

Keywords/Phrases

manifold, Poincaré space, singularity, controlled topology, chain duality

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