Resolution of smooth group actions

Details Resolution of smooth group actions Resolution of smooth group actions

2010-12-28

arxiv.org/abs/1012.5765v1

Proceedings of "Spectral Theory and Geometric Analysis" at Northeastern University, July 29 - August 2, 2009

Mathematics

Differential Geometry

First half of http://arxiv.org/abs/0907.3211v2, extensively rewritten

Scientific paper

A refined form of the `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a `resolution structure' consisting of equivariant iterated fibrations of the boundary faces. This structure projects to give a similar resolution structure for the quotient. In particular these results apply to give a canonical resolution of the radial compactification, to a ball, of any finite dimensional representation of a compact Lie group; such resolutions of the normal action of the isotropy groups appear in the boundary fibers in the general case.

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