A criterion for delooping the fibre of the self-map of a sphere with degree a power of a prime

H. Cejtin, S. Kleinerman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Fix, once and for all, p to be an odd prime, and n and j to be strictly positive integers. Let F be the homotopy fibre of the self-map of S2n-1 of degree pj is a fibration up to homotopy). Notice that F is its own localization at p. The sphere S2n-1 itself, localized at p, deloops if and only if n divides p -1. In [2], the second author showed that for certain values of p, n and j, the fibre F deloops. The deloopings are of the form BG(Fq)+(p) where G(Fq)is the universal Chevalley group of some exceptional Lie type over the finite field Fq, q a power of a prime different from p. Here "+" denotes Quillen’s "plus construction" (see [6]) and (p) denotes localization at the prime p. In all these cases n divides p- 1.

Original languageEnglish (US)
Pages (from-to)566-573
Number of pages8
JournalIllinois Journal of Mathematics
Volume30
Issue number4
DOIs
StatePublished - 1986

ASJC Scopus subject areas

  • Mathematics(all)

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