Geodesic
Singularities, double points, controlled topology and chain duality
Documenta mathematica, Tome 4 (1999), pp. 1-59
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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.
DOI : 10.4171/dm/52
Classification : 55N45, 55U35, 57R67
Mots-clés : singularity, manifold, Poincaré space, controlled topology, chain duality 
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     author = {Andrew Ranicki},
     title = {Singularities, double points, controlled topology and chain duality},
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     pages = {1--59},
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     doi = {10.4171/dm/52},
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Andrew Ranicki. Singularities, double points, controlled topology and chain duality. Documenta mathematica, Tome 4 (1999), pp. 1-59. doi: 10.4171/dm/52

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