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

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to