Tootfinder

Homology manifolds and homogeneous compacta
Vesko Valov
https://arxiv.org/abs/2505.07196 https://arxiv.org/pdf/2505.07196

Homology manifolds and homogeneous compacta
A non-trivial separable metric space $X$ is called an almost homology $n$-manifold if the homology groups $H_k(X,X\backslash\{x\},\mathbb Z)$ are trivial for all $x\in X$ and all $k=0,1,..,n-1$. We provide a necessary and sufficient condition locally compact homogeneous $ANR$-spaces or strongly locally homogeneous $ANR$-spaces to be almost homology $n$-manifolds.