{
  "id": "math/0403311",
  "version": "v3",
  "published": "2004-03-18T19:56:35.000Z",
  "updated": "2004-12-24T10:50:29.000Z",
  "title": "Circular groups, planar groups, and the Euler class",
  "authors": [
    "Danny Calegari"
  ],
  "comment": "Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper15.abs.html",
  "journal": "Geom. Topol. Monogr. 7 (2004) 431-491",
  "categories": [
    "math.GT",
    "math.DS",
    "math.GR"
  ],
  "abstract": "We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that certain generalized braid groups are circularly-orderable. We also show that the Euler class of C^infty diffeomorphisms of the plane is an unbounded class, and that any closed surface group of genus >1 admits a C^infty action with arbitrary Euler class. On the other hand, we show that Z oplus Z actions satisfy a homological rigidity property: every orientation-preserving C^1 action of Z oplus Z on the plane has trivial Euler class. This gives the complete homological classification of surface group actions on R^2 in every degree of smoothness.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-12-24T10:50:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C85",
      "37E30",
      "57M60"
    ],
    "keywords": [
      "circular groups",
      "planar groups",
      "arbitrary euler class",
      "trivial euler class",
      "surface group actions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3311C"
    }
  }
}