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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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Abstract

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
MIMS number:2008.90
Deposited By:Dr James Montaldi
Deposited On:19 July 2011

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