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Wrong way maps in uniformly finite homology and homology of groups

Research paper by Alexander Engel

Indexed on: 26 Oct '17Published on: 02 Sep '17Published in: Journal of Homotopy and Related Structures



Abstract

Given a non-compact Riemannian manifold M and a submanifold \(N \hookrightarrow M\) of codimension q, we will construct under certain assumptions on both M and N a wrong way map \(H^\mathrm {uf}_*(M) \rightarrow H^\mathrm {uf}_{*-q}(N)\) in uniformly finite homology. Using an equivariant version of the construction and applying it to universal covers, we will construct a map \(H_*(B\pi _1 M) \rightarrow H_{*-q}(B\pi _1 N)\). As applications we discuss obstructions to the existence of positive scalar curvature metrics and to inessentialness.