Geometry & Topology 7 (2003) 155–184

DOI: 10.2140/gt.2003.7.155

arXiv: math.AT/0304384

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 S¹–transfer map t:ΣCP^∞→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

Mathematical Subject Classification

Primary: 19D10

Secondary: 19F27, 55P42, 55Q52, 57R50, 57R80

References

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Publication

Received: 30 November 2001
Revised: 7 February 2003
Accepted: 13 March 2003
Published: 14 March 2003
Proposed: Haynes Miller
Seconded: Gunnar Carlsson, Thomas Goodwillie

Authors