{
  "id": "1005.0731",
  "version": "v1",
  "published": "2010-05-05T12:25:22.000Z",
  "updated": "2010-05-05T12:25:22.000Z",
  "title": "$L^2$-topology and Lagrangians in the space of connections over a Riemann surface",
  "authors": [
    "Tomasz S. Mrowka",
    "Katrin Wehrheim"
  ],
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform quasiconvexity of the gauge orbits. Using these, we generalize compactness results for anti-self-dual instantons with Lagrangian boundary counditions to general gauge invariant Lagrangian submanifolds. This provides the foundation for the construction of instanton Floer homology for pairs of a $3$-manifold with boundary and a Lagrangian in the configuration space over the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-05T12:25:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann surface",
      "general gauge invariant lagrangian submanifolds",
      "connections",
      "subtle local slice theorem",
      "gauge orbits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 854200,
      "adsabs": "2010arXiv1005.0731M"
    }
  }
}