Microbundles, manifolds and metrisability
by
Sina Greenwood
University of Auckland
Coauthors: David Gauld

The notion of a microbundle was introduced in the 1960's but the theory came to an abrupt halt when it was shown that, for a metrisable manifold, microbundles are equivalent to fibre bundles. However, this equivalence only holds for metrisable manifolds. We will show that for a Hausdorff n-manifold M, the following are equivalent:

1. M is metrisable.
2. The tangent microbundle over M is microbundle equivalent to a fibre bundle.
3. There is an open cover U of M such that for each x in M the set st(x, U) is homeomorphic to an open subset of Rⁿ.
4. There is an open cover U of M such that for each x in M the set st(x, U) is metrisable.
5. There is a cover A of M such that for each x in M the set st(x, A) is open and metrisable.

Date received: July 28, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caap-08.