Geodesic
Singularities, double points, controlled topology and chain duality
Documenta mathematica, Tome 4 (1999), pp. 1-59.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 55N45, 57R67, 55U35
Keywords: manifold, Poincaré space, singularity, controlled topology, chain duality 
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     author = {Ranicki, Andrew},
     title = {Singularities, double points, controlled topology and chain duality},
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Ranicki, Andrew. Singularities, double points, controlled topology and chain duality. Documenta mathematica, Tome 4 (1999), pp. 1-59. http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a19/