{
  "id": "1607.07499",
  "version": "v1",
  "published": "2016-07-25T22:42:05.000Z",
  "updated": "2016-07-25T22:42:05.000Z",
  "title": "A connected sum formula for involutive Heegaard Floer homology",
  "authors": [
    "Kristen Hendricks",
    "Ciprian Manolescu",
    "Ian Zemke"
  ],
  "comment": "53 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove a connected sum formula for involutive Heegaard Floer homology, and use it to study the involutive correction terms of connected sums. In particular, we give an example of a three-manifold with $\\underline{d}(Y) \\neq d(Y) \\neq \\overline{d}(Y)$. We also construct a homomorphism from the three-dimensional homology cobordism group to an algebraically defined Abelian group, consisting of certain complexes (equipped with a homotopy involution) modulo a notion of local equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-25T22:42:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57M27"
    ],
    "keywords": [
      "involutive heegaard floer homology",
      "connected sum formula",
      "three-dimensional homology cobordism group",
      "correction terms",
      "local equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}