Geometry & Topology, Vol. 7 (2003)
Paper no. 4, pages 155--184.
The smooth Whitehead spectrum of a point at odd regular primes
John Rognes
Abstract
Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen
conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type
of the smooth Whitehead spectrum Wh(*) is described. A suspended copy
of the cokernel-of-J spectrum splits off, and the torsion homotopy of
the remainder equals the torsion homotopy of the fiber of the
restricted S^1-transfer map t: SigmaCP^infty--> S. The homotopy groups
of Wh(*) are determined in a range of degrees, and the cohomology of
Wh(*) is expressed as an A-module in all degrees, up to an
extension. These results have geometric topological interpretations,
in terms of spaces of concordances or diffeomorphisms of highly
connected, high dimensional compact smooth manifolds.
Keywords. Algebraic K-theory, topological cyclic
homology, Lichtenbaum-Quillen conjecture, transfer, h-cobordism,
concordance, pseudoisotopy
AMS subject classification.
Primary: 19D10.
Secondary: 19F27, 55P42, 55Q52, 57R50, 57R80.
DOI: 10.2140/gt.2003.7.155
E-print: arXiv:math.AT/0304384
Submitted to GT on 30 November 2001.
(Revised 7 February 2003.)
Paper accepted 13 March 2003.
Paper published 14 March 2003.
Notes on file formats
John Rognes
Department of Mathematics, University of Oslo
N--0316 Oslo, Norway
Email: rognes@math.uio.no
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