Volume 13, issue 4 (2013)

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
$\mathit{UV}^k$–mappings on homology manifolds

John Bryant, Steve Ferry and Washington Mio

Algebraic & Geometric Topology 13 (2013) 2141–2170
Abstract

We prove a strong controlled generalization of a theorem of Bestvina and Walsh, which states that a $\left(k+1\right)$–connected map from a topological $n$–manifold to a polyhedron, $2k+3\le n$, is homotopic to a ${UV}^{k}$–map, that is, a surjection whose point preimages are, in some sense, $k$–connected. One consequence of our main result is that a compact ENR homology $n$–manifold, $n\ge 5$, having the disjoint disks property satisfies the linear ${UV}^{⌊\left(n-3\right)∕2⌋}$–approximation property for maps to compact ANRs. The method of proof is general enough to show that any compact ENR satisfying the disjoint $\left(k+1\right)$–disks property has the linear ${UV}^{k}$–approximation property.

Keywords
absolute neighborhood retract, homology manifolds, $UV^k$–mappings
Mathematical Subject Classification 2010
Primary: 57Q35, 57Q30, 57N99, 57P99
Publication
Revised: 31 December 2012
Accepted: 9 January 2013
Published: 6 June 2013
Authors
 John Bryant Department of Mathematics Florida State University Tallahassee, FL 32306 USA Steve Ferry Department of Math Sciences Rutgers University Piscataway, NJ 08854-8019 USA Washington Mio Department of Mathematics Florida State University Tallahassee, FL 32306 USA