Resolution of smooth group actions
Author(s)Albin, Pierre; Melrose, Richard B.
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Spectral theory and geometric analysis
American Mathematical Society
Albin, Pierre and Richard Melrose. "Resolution of smooth group actions." In p.1-26. Mazim Braverman, et al (Eds.), Spectral theory and geometric analysis: an international conference in honor of Mikhail Shubins's 65th birthday, July 29-August 2, 2009, Northeastern University, Boston, Massachusetts. (Contemporary mathematics; v. 535).
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