Applications of controlled surgery in dimension 4 : Examples

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The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The goal of this paper is to show that this also holds for other fundamental groups which are not known to be good, and that it is best understood using controlled surgery theory of Pedersen-Quinn-Ranicki. We consider some examples of 4-manifolds which have the fundamental group either of a closed aspherical surface or of a 3-dimensional knot space. A more general theorem is stated in the appendix.

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 58(4), 1151-1162, 2006-10-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10018380875
  • 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
    8512867
  • 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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