Desingularizing homology manifolds

Bryant, J L; Ferry, Steven; Mio, Washington; Weinberger, Shmuel

doi:10.2140/gt.2007.11.1289

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Desingularizing homology manifolds

J Bryant, S Ferry, W Mio and S Weinberger

Geometry & Topology 11 (2007) 1289–1314

DOI: 10.2140/gt.2007.11.1289

Abstract

We prove that if $X^{n}$ , $n \geq 6$ , 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 $f : Y \to X$ .

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

Volume 11, issue 3 (2007)