# 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.