{
  "id": "1505.06778",
  "version": "v1",
  "published": "2015-05-25T23:31:52.000Z",
  "updated": "2015-05-25T23:31:52.000Z",
  "title": "On the topological Hochschild homology of $DX$",
  "authors": [
    "Cary Malkiewich"
  ],
  "comment": "61 pages. Represents part of the author's thesis",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "We begin a systematic study of the topological Hochschild homology of the commutative ring spectrum $DX$, the dual of a finite CW-complex $X$. We prove that the \"Atiyah duality\" between $THH(DX)$ and the free loop space $\\Sigma^\\infty_+ LX$ is an $S^1$-equivariant duality that preserves the $C_n$-fixed points, in addition to the ring structure and Adams operations. We then prove a stable splitting on $THH(D\\Sigma X)$, and use this to calculate $THH(DS^{2n+1})$ and $TC(DS^1)$. Our approach uses a new, simplified construction of $THH$ due to Angeltveit et al., building on the work of Hill, Hopkins, and Ravenel. We also extend and elucidate this new model of $THH$, using a simple but powerful rigidity theorem for the geometric fixed point functor $\\Phi^G$ of orthogonal $G$-spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T23:31:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19D55",
      "55P25",
      "55P43",
      "55P91"
    ],
    "keywords": [
      "topological hochschild homology",
      "free loop space",
      "geometric fixed point functor",
      "systematic study",
      "equivariant duality"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506778M"
    }
  }
}