principal bundle
Let be a topological space on which a topological group acts continuously and freely. The map is called a principal bundle (or principal -bundle) if the projection map is a locally trivial bundle.
Any principal bundle with a section is trivial, since the map given by is an isomorphism. In particular, any -bundle which is topologically trivial is also isomorphic to as a -space. Thus any local trivialization of as a topological bundle is an equivariant trivialization.
Title | principal bundle |
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Canonical name | PrincipalBundle |
Date of creation | 2013-03-22 13:07:18 |
Last modified on | 2013-03-22 13:07:18 |
Owner | rmilson (146) |
Last modified by | rmilson (146) |
Numerical id | 8 |
Author | rmilson (146) |
Entry type | Definition |
Classification | msc 55R10 |
Defines | principal G-bundle |