The equivariant J–homomorphism for finite groups at certain primes

French, Christopher P¹

¹Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112, United States

Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 1885-1949

Résumé

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.

Détail

DOI : 10.2140/agt.2009.9.1885

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

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