Proper actions and decompositions in equivariant K-theory
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909308054142976 |
|---|---|
| author | Angel, Andrés Becerra, Edward Velásquez, Mario |
| author_facet | Angel, Andrés Becerra, Edward Velásquez, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_09777 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Proper actions and decompositions in equivariant K-theory Angel, Andrés Becerra, Edward Velásquez, Mario Algebraic Topology K-Theory and Homology Representation Theory 55N15, 19L50, 19L47, 19L41, 55N20 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. |
| title | Proper actions and decompositions in equivariant K-theory |
| topic | Algebraic Topology K-Theory and Homology Representation Theory 55N15, 19L50, 19L47, 19L41, 55N20 |
| url | https://arxiv.org/abs/2003.09777 |