Notes on lifting group actions

Montaldi, James and Ortega, Juan-Pablo (2008) Notes on lifting group actions. [MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User:	Dr James Montaldi
Date Deposited:	19 Jul 2011
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1158

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