Equivariant Resolution, Cohomology and Index Joint Work with Pierre Albin for Werner Müller’s 60th Birthday
نویسنده
چکیده
In this talk I describe the resolution to unique isotropy type of the smooth action of a compact Lie group as contained in joint work with Pierre Albin, [2], [3]. The resulting ‘resolution tower’ leads to resolved and reduced models for equivariant cohomology, including the delocalized cohomology of Baum, Brylinski and MacPherson, and K-theory. Combining these constructions with a lifting map gives a families version of the pseudodifferential equivariant index theorem of Atiyah and Singer with corresponding representations of the Chern character.
منابع مشابه
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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 tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...
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