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  "body": "\n## Summary\n\nA homology $n$-manifold is a space whose local homology at every point is that of a point in $\\R^n$.\nEvery [[topological manifold|QQQ9B1DK4P]] is a homology manifold, but there are homology manifolds that are not manifolds.\nPoincaré duality holds for compact oriented homology manifolds, so they are the natural setting for many results first proved for manifolds.\n\n## Explanations\n\n### L1 human\n\nNear any point of an $n$-dimensional manifold, the space looks like $\\R^n$.\nHomology cannot see the whole shape of a neighbourhood, only some of its features, such as the holes left when the point is removed.\nA homology manifold is a space where, near every point, these features are the same as in $\\R^n$.\nFor example, take the cone over a space with the homology of a sphere but a nontrivial fundamental group.\nIt passes this test at its tip, though it is not a manifold there.\n",
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