Volume 11, issue 3 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Desingularizing homology manifolds

J Bryant, S Ferry, W Mio and S Weinberger

Geometry & Topology 11 (2007) 1289–1314
Abstract

We prove that if Xn , n 6, is a compact ANR homology n–manifold, we can blow up the singularities of X to obtain an ANR homology n–manifold with the disjoint disks property. More precisely, we show that there is an ANR homology n–manifold Y with the disjoint disks property and a cell-like map f : Y X.

Keywords
homology manifold, cell-like map, controlled topology
Mathematical Subject Classification 2000
Primary: 57N15, 57P99
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Publication
Received: 6 October 2005
Revised: 14 February 2007
Accepted: 8 September 2006
Published: 20 July 2007
Proposed: Rob Kirby
Seconded: Peter Teichner and Wolfgang Lueck
Authors
J Bryant
Department of Mathematics
Florida State University
Tallahassee FL 32306
USA
S Ferry
Department of Mathematical Sciences
Rutgers University
Piscataway NJ 08854
USA
http://math.rutgers.edu/~sferry/
W Mio
Department of Mathematics
Florida State University
Tallahassee FL 32306
USA
S Weinberger
Department of Mathematics
The University of Chicago
Chicago IL 60637
USA