Abstract
We prove a strong controlled generalization of a theorem of Bestvina and Walsh, which states that a –connected map from a topological –manifold to a polyhedron, , is homotopic to a –map, that is, a surjection whose point preimages are, in some sense, –connected. One consequence of our main result is that a compact ENR homology –manifold, , having the disjoint disks property satisfies the linear –approximation property for maps to compact ANRs. The method of proof is general enough to show that any compact ENR satisfying the disjoint –disks property has the linear –approximation property.
Citation
John Bryant. Steve Ferry. Washington Mio. "$\mathit{UV}^k$–mappings on homology manifolds." Algebr. Geom. Topol. 13 (4) 2141 - 2170, 2013. https://doi.org/10.2140/agt.2013.13.2141
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