Microbundles Revisited
by
David Gauld
University of Auckland
Coauthors: Sina Greenwood

In [2] Milnor introduced the notion of a microbundle. Amongst other things it provided a means of transferring some of the procedures applicable to bundles over smooth manifolds to manifolds which are not necessarily smooth. The development of the theory came to an abrupt halt with the appearance of [1] which shows that for paracompact (equivalently metrisable) manifolds microbundles are equivalent to fibre bundles. In this paper we consider whether microbundles are equivalent to fibre bundles when the base manifold is not metrisable. We show that the tangent microbundle (as defined in [2]) over the long line is not equivalent to a fibre bundle.

1 J. M. Kister Microbundles are fibre bundles Ann Math 80 2 1964 190-199
2 J. Milnor Microbundles Part I Topology 3 Suppl 1 1964 53-80

Date received: June 24, 1996

Copyright © 1996 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 # caah-22.