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Involutions Fixing Fn ∪ ﹛Indecomposable﹜

  • Pedro L. Q. Pergher (a1)
Abstract

Let Mm be an m-dimensional, closed and smooth manifold, equipped with a smooth involution T : Mm Mm whose fixed point set has the form Fn Fj , where Fn and Fj are submanifolds with dimensions n and j, Fj is indecomposable and n > j. Write nj = 2 pq, where q ≥ 1 is odd and p ≥ 0, and set m(nj) = 2n + pq +1 if pq +1 and m(nj) = 2n +2 p q if pq. In this paper we show that mm(nj) + 2j + 1. Further, we show that this bound is almost best possible, by exhibiting examples (Mm (nj)+2j , T) where the fixed point set of T has the form Fn Fj described above, for every 2 ≤ j < n and j not of the form 2 t – 1 (for j = 0 and 2, it has been previously shown that m(nj) + 2 j is the best possible bound). The existence of these bounds is guaranteed by the famous 5/2-theorem of J. Boardman, which establishes that under the above hypotheses .

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References
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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