Rational self-equivalences of spaces in the genus of a product of quaternionic projective spaces

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For G=S3וs× S3, let X be a space such that the p-completion (X)p^ is homotopy equivalent to (BG)p^ for any prime p. We investigate the monoid of rational equivalences of X, denoted by ε0(X). This topological question is transformed into a matrix problem over Qotimes Z^, since ε0(BG) is the set of monomial matrices whose nonzero entries are odd squares. It will be shown that a submonoid of ε0(X), denoted by δ0(X), determines the decomposability of X. Namely, if Nodd denotes the monoid of odd natural numbers, Theorem 2 shows that the monoid δ0(X) is isomorphic to a direct sum of copies of Nodd. Moreover the space X splits into m indecomposable spaces if and only if δ0(X)_??_(Nodd)m. When such a space X is indecomposable, the relationship between [X, X] and [BG, BG] is discussed. Our results indicate that the homotopy set [X, X] contains less maps if X is not homotopy equivalent to the product of quaternionic projective spaces BG=HP∈ftyוs× HP∈fty.

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 51(1), 45-61, 1999-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10002151365
  • 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
    4643257
  • 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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