 Homology manifold

In mathematics, a homology manifold (or generalized manifold)
is a locally compact topological space "X" that looks locally like a topological manifold from the point of view of homology theory.A homology "G"-manifold (without boundary) of dimension "n" over an abelian group "G" of coefficients is a locally compact topological space X with finite "G"-cohomological dimension such that for any "x"∈"X", the homology groups
are trivial unless "p"="n", in which case they are isomorphic to "G".