UVk-mappings on homology manifolds

Bryant, John¹ ; Ferry, Steve² ; Mio, Washington¹

¹Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA
²Department of Math Sciences, Rutgers University, Piscataway, NJ 08854-8019, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2141-2170

Résumé

We prove a strong controlled generalization of a theorem of Bestvina and Walsh, which states that a (k + 1)–connected map from a topological n–manifold to a polyhedron, 2k + 3 ≤ 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 ≥ 5, having the disjoint disks property satisfies the linear UV ⌊(n−3)∕2⌋–approximation property for maps to compact ANRs. The method of proof is general enough to show that any compact ENR satisfying the disjoint (k + 1)–disks property has the linear UV k–approximation property.

Détail

DOI : 10.2140/agt.2013.13.2141

Classification : 57Q35, 57Q30, 57N99, 57P99
Keywords: absolute neighborhood retract, homology manifolds, $UV^k$–mappings

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