On the stable cohomology algebra of extended mapping class groups for surfaces

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説明

Let :E0,1 be an oriented compact surface of genus g with 1 boundary component, and r g,1 the mapping·class group of :Eg,1 · We determine the stable cohomology group of r 0,1 with coefficients in H1 (:Eg,1; Z)®n, n 􀀥 l, explicitly modulo the stable cohomology group with trivial coefficients. As a corollary the rational stable cohomology algebra of the semi-direct product r g,1 1>< H1 (:E0,1; Z) (which we call the extended mapping class group) is proved to be freely generated by the generalized Morita-Mumford classes in;J 's (i 􀀵 0, j 􀀵 1, i + j 􀀵 2) [Ka) over the rational stable cohomology algebra of the group r g,1 •

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詳細情報 詳細情報について

  • CRID
    1390009224795169280
  • NII論文ID
    120006456614
  • DOI
    10.14943/83458
  • HANDLE
    2115/69062
  • 本文言語コード
    en
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • JaLC
    • IRDB
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用可

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