{
  "id": "0806.1572",
  "version": "v3",
  "published": "2008-06-10T05:43:38.000Z",
  "updated": "2011-09-24T01:25:56.000Z",
  "title": "Comparing 2-handle additions to a genus 2 boundary component",
  "authors": [
    "Scott A. Taylor"
  ],
  "comment": "Paper completely rewritten. Main sutured manifold theory results have been moved to a separate paper",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that knots obtained by attaching a band to a split link satisfy the cabling conjecture. We also give new proofs that unknotting number one knots are prime and that genus is superadditive under band sum. Additionally, we prove a collection of results comparing two 2-handle additions to a genus two boundary component of a compact, orientable 3-manifold. These results give a near complete solution to a conjecture of Scharlemann and provide evidence for a conjecture of Scharlemann and Wu. The proofs make use of a new theorem concerning the effects of attaching a 2-handle to a suture in the boundary of a sutured manifold.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-24T01:25:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M50"
    ],
    "keywords": [
      "boundary component",
      "split link satisfy",
      "band sum",
      "complete solution",
      "scharlemann"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1572T"
    }
  }
}