Algebraic & Geometric Topology

The equivariant $J$–homomorphism for finite groups at certain primes

Christopher P French

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Suppose G is a finite group and p a prime, such that none of the prime divisors of G are congruent to 1 modulo p. We prove an equivariant analogue of Adams’ result that J=J. We use this to show that the G–connected cover of QGS0, when completed at p, splits up to homotopy as a product, where one of the factors of the splitting contains the image of the classical equivariant J–homomorphism on equivariant homotopy groups.

Article information

Algebr. Geom. Topol., Volume 9, Number 4 (2009), 1885-1949.

Received: 7 May 2007
Revised: 17 July 2009
Accepted: 3 August 2009
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 19L20: $J$-homomorphism, Adams operations [See also 55Q50] 19L47: Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] 55R91: Equivariant fiber spaces and bundles [See also 19L47]

$J$–homomorphism Adams operations equivariant $K$–theory equivariant fiber spaces and bundles


French, Christopher P. The equivariant $J$–homomorphism for finite groups at certain primes. Algebr. Geom. Topol. 9 (2009), no. 4, 1885--1949. doi:10.2140/agt.2009.9.1885.

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