{
  "id": "2006.09669",
  "version": "v1",
  "published": "2020-06-17T05:49:26.000Z",
  "updated": "2020-06-17T05:49:26.000Z",
  "title": "Equivariant cohomology for cyclic groups of square-free order",
  "authors": [
    "Samik Basu",
    "Surojit Ghosh"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "The main objective of this paper is to compute $RO(G)$-graded cohomology of $G$-orbits for the group $G=C_n$, where $n$ is a product of distinct primes. We compute these groups for the constant Mackey functor $\\underline{Z}$ and for the Burnside ring Mackey functor $\\underline{A}$. Among other things, we show that the groups $\\underline{H}^\\alpha_G(S^0)$ are mostly determined by the fixed point dimensions of the virtual representations $\\alpha$, except in the case of $\\underline{A}$ coefficients when the fixed point dimensions of $\\alpha$ have many zeros. In the case of $\\underline{Z}$ coefficients, the ring structure on the cohomology is also described. The calculations are then used to prove freeness results for certain $G$-complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-17T05:49:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic groups",
      "square-free order",
      "equivariant cohomology",
      "fixed point dimensions",
      "burnside ring mackey functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}