UVk-mappings on homology manifolds

作者：Bryant John^*; Ferry Steve; Mio Washington

来源：Algebraic and Geometric Topology, 2013, 13(4): 2141-2170.

DOI：10.2140/agt.2013.13.2141

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 %26lt;= n, is homotopic to a UVk-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 %26gt;= 5, having the disjoint disks property satisfies the linear UVleft perpendicular(n-3)/2right perpendicular-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 UVk-approximation property.

• 出版日期2013