{
  "id": "1805.02563",
  "version": "v1",
  "published": "2018-05-07T15:14:40.000Z",
  "updated": "2018-05-07T15:14:40.000Z",
  "title": "A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces",
  "authors": [
    "Naoya Enomoto",
    "Yusuke Kuno",
    "Takao Satoh"
  ],
  "comment": "17 pages",
  "categories": [
    "math.GT",
    "math.AT",
    "math.RT"
  ],
  "abstract": "In [ES2], the first and the third authors introduced new classes in the Johnson cokernels of the mapping class groups of surfaces by a representation theoretic approach based on some previous results for the Johnson cokernels of the automorphism groups of free groups. On the other hand, in [KK1], Kawazumi and the second author introduced another type of classes by a topological consideration of self-intersections of curves on a surface. In this paper, we show that the classes found in [KK1] are contained in the classes found in [ES2] in a stable range. Furthermore, we prove that the anti-Morita obstructions $[1^{4m+1}]$ for $m \\ge 1$ obtained in [ES2] and a hook-type component $[3,1^5]$ detected in [EE] appear in their gap.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-07T15:14:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class groups",
      "johnson cokernels",
      "comparison",
      "representation theoretic approach",
      "third authors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}