{
  "id": "1105.3028",
  "version": "v1",
  "published": "2011-05-16T08:18:41.000Z",
  "updated": "2011-05-16T08:18:41.000Z",
  "title": "Equivariant Kasparov theory of finite groups via Mackey functors",
  "authors": [
    "Ivo Dell'Ambrogio"
  ],
  "comment": "28 pages",
  "categories": [
    "math.OA",
    "math.KT"
  ],
  "abstract": "Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a separable G-C*-algebra the collection of all its equivariant K-theory groups lifts naturally to a homological functor taking values in the abelian tensor category of Mackey modules over the classical representation Green functor for G. This fact yields a new universal coefficient and a new Kuenneth spectral sequence for the G-equivariant Kasparov category, whose convergence behavior is nice for all G-C*-algebras in a certain bootstrap class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-16T08:18:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L80",
      "46M18",
      "19A22"
    ],
    "keywords": [
      "equivariant kasparov theory",
      "finite group",
      "mackey functors",
      "equivariant k-theory groups lifts",
      "systematically exploit general homological methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3028D"
    }
  }
}