On the nonuniqueness of equivariant connected sums

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In both ordinary and equivariant 3-dimensional topology there are strong uniqueness theorems for connected sum decompositions of manifolds, but in ordinary higher dimensional topology such decompositions need not be unique. This paper constructs families of manifolds with smooth group actions that are equivariantly almost diffeomorphic but have infinitely many inequivalent equivariant connected sum repre-sentations for which one summand is fixed. The examples imply the need for restrictions in any attempt to define Atiyah-Singer type invariants for odd dimensional manifolds with nonfree smooth group actions. Applications to other questions are also considered.

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 51(2), 413-435, 1999-04 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10002151712
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    4712219
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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