WILDER MANIFOLDS ARE LOCALLY ORIENTABLE

1 August 1969

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 63 (4) , 1079-1081
https://doi.org/10.1073/pnas.63.4.1079

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.

Keywords

MANIFOLD
LOCAL ORIENTABILITY
HOMOLOGY GROUPS
LOCAL HOMOLOGY
LONG STANDING
STANDING CONJECTURE
LOCALLY COMPACT
COMPACT SPACE
NICE RELATIONSHIP

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