The study finds essential conditions for locally compact homogeneous metric spaces to be almost homology n-manifolds, suggesting implications for topology.
A non-trivial separable metric space X is called an almost homology n-manifold if the homology groups Hₖ(X,X\, Z) are trivial for all x∈ 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.
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Vesko Valov (2025) studied this question.
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