Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 4 (2009), 1885-1949.
The equivariant $J$–homomorphism for finite groups at certain primes
Suppose is a finite group and a prime, such that none of the prime divisors of are congruent to modulo . We prove an equivariant analogue of Adams’ result that . We use this to show that the –connected cover of , when completed at , splits up to homotopy as a product, where one of the factors of the splitting contains the image of the classical equivariant –homomorphism on equivariant homotopy groups.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
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. https://projecteuclid.org/euclid.agt/1513797069