Translator Disclaimer
2003 The smooth Whitehead spectrum of a point at odd regular primes
John Rognes
Geom. Topol. 7(1): 155-184 (2003). DOI: 10.2140/gt.2003.7.155


Let p be an odd regular prime, and assume that the Lichtenbaum–Quillen conjecture holds for K([1p]) 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:ΣPS. 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.


Download Citation

John Rognes. "The smooth Whitehead spectrum of a point at odd regular primes." Geom. Topol. 7 (1) 155 - 184, 2003.


Received: 30 November 2001; Revised: 7 February 2003; Accepted: 13 March 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1130.19300
MathSciNet: MR1988283
Digital Object Identifier: 10.2140/gt.2003.7.155

Primary: 19D10
Secondary: 19F27, 55P42, 55Q52, 57R50, 57R80

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.7 • No. 1 • 2003
Back to Top