Microbundles, manifolds and metrisability
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- by David Gauld and Sina Greenwood PDF
- Proc. Amer. Math. Soc. 128 (2000), 2801-2807 Request permission
Abstract:
The notion of a microbundle was introduced in the 1960s but the theory came to an abrupt halt when it was shown that for a metrisable manifold, microbundles are equivalent to fibre bundles. In this paper we consider microbundles over non-metrisable manifolds. In some cases microbundles are equivalent to fibre bundles but in others they are not. In particular, we show that a manifold is metrisable if and only if its tangent microbundle is equivalent to a fibre bundle. We also illustrate that for some non-metrisable manifolds every trivial microbundle contains a trivial fibre bundle whereas other manifolds may support a trivial microbundle not containing a trivial fibre bundle.References
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Additional Information
- David Gauld
- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
- Email: gauld@math.auckland.ac.nz
- Sina Greenwood
- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
- Email: sina@math.auckland.ac.nz
- Received by editor(s): July 8, 1997
- Received by editor(s) in revised form: October 16, 1998
- Published electronically: March 1, 2000
- Additional Notes: The second author’s research was supported in part by a Marsden Fund Award, UOA611
- Communicated by: Alan Dow
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2801-2807
- MSC (2000): Primary 57N55, 54E35, 55R60, 57N05, 57N15
- DOI: https://doi.org/10.1090/S0002-9939-00-05343-0
- MathSciNet review: 1664358