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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

Abstract

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.

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John Rognes. "The smooth Whitehead spectrum of a point at odd regular primes." Geom. Topol. 7 (1) 155 - 184, 2003. https://doi.org/10.2140/gt.2003.7.155

Information

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

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

Rights: Copyright © 2003 Mathematical Sciences Publishers

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