The smooth Whitehead spectrum of a point at odd regular primes

2003/04/24 by John Rognes · 1 citation
Mathematics · #math.AT #math.GT #msc:19D10 #msc:19F27 #msc:55P42 #msc:55Q52 #msc:57R50 #msc:57R80

paper · pdf · doi:10.2140/gt.2003.7.155

published as Geom. Topol. 7 (2003) 155-184 · Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper4.abs.html

arxiv created 2003/04/24 · arxiv updated 2014/11/11

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: SigmaCPⁱnfty--> 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.

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