Fundmental class of a homology manifold

Suppose $X$ is a compact, connected $n$-dimensional homology ($\Bbb Z$-)manifold (https://en.wikipedia.org/wiki/Homology_manifold). Since orientability is defined using only homology (for example, in Hatcher's book), we can define orientability of homology manifolds. Suppose $X$ is orientable. Then is it true that there is a fundamental class of $X$?

Orientable closed, connected manifolds have fundamental classes (Theorem 3.26 in Hatcher https://pi.math.cornell.edu/~hatcher/AT/AT.pdf), but the proof uses the local Euclidean condition of manifolds, so the proof doesn't apply directly to homology manifolds.

Solution 1:

References for Poincare Duality for orientable $L$-homology manifolds, where $L$ is a PID are:

A. Borel, "The Poincaré duality in generalized manifolds" Michigan Math. J., 4 (1957) pp. 227–239.

A. Borel, "Homology and duality in generalized manifolds" A. Borel (ed.), Seminar on transformation groups, Princeton Univ. Press (1960) pp. 23–33.

Another reference is Bredon's book "Sheaf theory" but I find it unreadable.

From these, you get the fundamental class and much more, of course.