{
  "id": "2403.08116",
  "version": "v1",
  "published": "2024-03-12T22:56:41.000Z",
  "updated": "2024-03-12T22:56:41.000Z",
  "title": "Cyclic homology of categorical coalgebras and the free loop space",
  "authors": [
    "Manuel Rivera",
    "Daniel Tolosa"
  ],
  "categories": [
    "math.AT",
    "math.QA"
  ],
  "abstract": "We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an arbitrary topological space $X$ is naturally quasi-isomorphic to the $S^1$-equivariant chains of free loop space of $X$. This statement does not require any hypotheses on $X$ or on the commutative ring of coefficients. Along the way, we introduce a family of polytopes, coined as Goodwillie polytopes, that controls the combinatorics behind the relationship of the coHochschild complex of a categorical coalgebra and the Hochschild complex of its associated differential graded category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-12T22:56:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free loop space",
      "categorical coalgebra",
      "cyclic homology",
      "cyclic chain complex",
      "arbitrary topological space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}