{
  "id": "1605.06266",
  "version": "v1",
  "published": "2016-05-20T09:55:55.000Z",
  "updated": "2016-05-20T09:55:55.000Z",
  "title": "Invariants under deformation of the actions of topological groups",
  "authors": [
    "Andrés Viña"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $\\varphi$ and $\\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\\varphi}(X)$ of $X$ relative to the action $\\varphi$ we associate an object $A'$ of category $D_{\\varphi'}(X)$, such that the corresponding $G$-equivariant compactly supported cohomologies $H_{G,c}(X,\\,A)$ and $H_{G,c}(X,\\,A')$ are isomorphic. When $G$ is a Lie group and $X$ is a subanalytic space, we prove that the $G$-equivariant cohomologies $H_{G}(X,\\,A)$ and $H_{G}(X,\\,A')$ are also isomorphic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-20T09:55:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological group",
      "invariants",
      "deformation",
      "lie group",
      "homotopic actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}