TY - JOUR

T1 - A criterion for delooping the fibre of the self-map of a sphere with degree a power of a prime

AU - Cejtin, H.

AU - Kleinerman, S.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

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U2 - 10.1215/ijm/1256064231

DO - 10.1215/ijm/1256064231

M3 - Article

AN - SCOPUS:84972564370

SN - 0019-2082

VL - 30

SP - 566

EP - 573

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 4

ER -