{
  "id": "1812.06781",
  "version": "v1",
  "published": "2018-12-13T21:22:31.000Z",
  "updated": "2018-12-13T21:22:31.000Z",
  "title": "Homological Stability for Spaces of Subsurfaces with Tangential Structure",
  "authors": [
    "Thorben Kastenholz"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1304.3006 by other authors",
  "categories": [
    "math.AT"
  ],
  "abstract": "Given a closed, simply connected and at least $5$-dimensional manifold $M$ together with some $p\\in M$ and a two-plane $A$ in $T_pM$, one can consider the space of submanifolds of $M$ that are diffeomorphic to a surface of genus $g$ and that meet $p$ tangential to $A$. We introduce a notion of tangential structure for these subsurfaces and construct a stabilization map for these spaces of subsurfaces which increases the genus by $1$. Then we proceed to prove homological stability for these stabilization maps. As an application of this general result we prove homological stability for spaces of symplectic subsurfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-13T21:22:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homological stability",
      "tangential structure",
      "stabilization map",
      "symplectic subsurfaces",
      "general result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}