Wilder manifolds are locally orientable.
A proof is given for the long-standing conjecture of R. L. Wilder that every generalized manifold is locally orientable. Roughly speaking, a generalized n-manifold is a locally compact space whose local homology groups at each point are those of an n-manifold. Local orientability is a condition in which the local homology groups at neighboring points have a certain nice relationship to one another. Local orientability is indispensable for almost all applications.
RUTGERS UNIVERSITY, NEW BRUNSWICK, NEW JERSEY.
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Bredon