WILDER MANIFOLDS ARE LOCALLY ORIENTABLE

Abstract

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.