2008.90: Notes on lifting group actions
2008.90: James Montaldi and Juan-Pablo Ortega (2008) Notes on lifting group actions.
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Given an action of a Lie group G on a manifold M, and a cover N of M (such as the universal cover M-tilde) the natural question arises of whether the action lifts to a cover of M. In these notes, we address this question and determine whether the G-action itself lifts or whether it is necessary to pass to a cover of G (there is always a lift of the action of the universal cover G-tilde). The results are presumably well-known to experts, but do not seem to be available in print.
These notes started life as the first section of a paper on symplectic (but non-hamiltonian) group actions, though it was felt that they were too detailed for a paper primarily on symplectic reduction. We are therefore making them available as a MIMS preprint.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||Group actions, universal cover,|
|Subjects:||MSC 2000 > 53 Differential geometry|
MSC 2000 > 58 Global analysis, analysis on manifolds
|Deposited By:||Dr James Montaldi|
|Deposited On:||19 July 2011|