On the homotopy groups of the self-equivalences of linear spheres

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Abstract

Let S(V ) be a complex linear sphere of a finite group G. LetS(V )∗n denote the n-fold join of S(V ) with itself and let autG(S(V )∗)denote the space of G-equivariant self homotopy equivalences of S(V )∗n.We show that for any k ≥ 1 there exists M > 0 which depends only onV such that |k autG(S(V )∗n)| ≤ M is for all n ≫ 0.
Original languageEnglish
Pages (from-to)445-462
Number of pages18
JournalProceedings of the Edinburgh Mathematical Society
Volume59
Issue number2
Early online date26 Oct 2015
DOIs
Publication statusPublished - May 2016

Keywords

  • homotopy groups
  • self-equivalences
  • equivariant spheres
  • complex representations

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