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Abstract
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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.
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Keywords
$J$–homomorphism, Adams operations, equivariant $K$–theory,
equivariant fiber spaces and bundles
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Mathematical Subject Classification 2000
Primary: 19L20, 19L47, 55R91
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Publication
Received: 7 May 2007
Revised: 17 July 2009
Accepted: 3 August 2009
Published: 3 October 2009
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