Volume 9, issue 4 (2009)

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

Christopher P French

Algebraic & Geometric Topology 9 (2009) 1885–1949
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 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.

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/