{
  "id": "2407.20082",
  "version": "v1",
  "published": "2024-07-29T15:06:48.000Z",
  "updated": "2024-07-29T15:06:48.000Z",
  "title": "Reflexive homology and involutive Hochschild homology as equivariant Loday constructions",
  "authors": [
    "Ayelet Lindenstrauss",
    "Birgit Richter"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We prove that for commutative rings whose underlying abelian group is flat and in which $2$ is invertible, the homotopy groups at the trivial orbit of the equivariant Loday construction of the one-point compactification of the sign-representation are isomorphic to reflexive homology as studied by Graves and to involutive Hochschild homology defined by Fern\\`andez-al\\`encia and Giansiracusa. We also show a relative version of these results for commutative $k$-algebras $R$ with involution, whenever $2$ is invertible in $R$ and $R$ is flat as a $k$-module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-29T15:06:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivariant loday construction",
      "involutive hochschild homology",
      "reflexive homology",
      "one-point compactification",
      "trivial orbit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}