An equivariant index for proper actions II: Properties and applications
نویسندگان
چکیده
منابع مشابه
Equivariant K-theory, Groupoids and Proper Actions
In this paper we define complex equivariantK-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid G, this defines a periodic cohomology theory on the category of finite G-CW-complexes. A suitable groupoid allows us to define complex equivariant K-theory for proper actions of non-compact Lie groups, which is a natural extension of the theory defined in [24]. For the particul...
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Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalised coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...
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LetG be a discrete group and letX be aG-finite, properG-CW-complex. We prove that Kasparov’s equivariant K-homology groups KK∗ (C0(X),C) are isomorphic to the geometric equivariant K-homology groups of X that are obtained by making the geometric K-homology theory of Baum and Douglas equivariant in the natural way. This reconciles the original and current formulations of the Baum-Connes conjectu...
متن کاملTwisted Equivariant K-theory, Groupoids and Proper Actions
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ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2018
ISSN: 1661-6952
DOI: 10.4171/jncg/273