Proper actions and decompositions in equivariant K-theory
| Autor: | Angel, Andrés, Becerra, Edward, Velásquez, Mario |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we study a natural decomposition of $G$-equivariant $K$-theory of a proper $G$-space, when $G$ is a Lie group with a compact normal subgroup $A$ acting trivially. Our decomposition could be understood as a generalization of the theory known as Mackey machine under suitable hypotheses, since it decomposes $G$-equivariant K-theory in terms of twisted equivariant K-theory groups respect to some subgroups of $G/A$. Similar decompositions were known for the case of a compact Lie group acting on a space, but our main result applies to discrete, linear and almost connected groups. We also apply this decomposition to study equivariant $K$-theory of spaces with only one isotropy type. We provide a rich class of examples in order to expose the strength and generality of our results. We also study the decomposition for equivariant connective $K$-homology for actions of compact Lie groups using a suitable configuration space model, based on previous papers published by the third author. Comment: 33 pages (this version) |
| Databáze: | arXiv |
| Externí odkaz: |
|