2008.90: Notes on lifting group actions

2008.90: James Montaldi and Juan-Pablo Ortega (2008) Notes on lifting group actions.

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 84 Kb

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.

Download Statistics: last 4 weeks
Repository Staff Only: edit this item