The equivariant J–homomorphism for finite groups at certain primes

French, Christopher P

doi:10.2140/agt.2009.9.1885

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

Christopher P French

Algebraic & Geometric Topology 9 (2009) 1885–1949

DOI: 10.2140/agt.2009.9.1885

Abstract

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 $Q_{G} S^{0}$ , 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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 19L20, 19L47, 55R91

References

Publication

Received: 7 May 2007

Revised: 17 July 2009

Accepted: 3 August 2009

Published: 3 October 2009

Authors

Christopher P French
Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 United States
http://www.math.grin.edu/~frenchc/

Volume 9, issue 4 (2009)