Geometry & Topology
- Geom. Topol.
- Volume 7, Number 1 (2003), 155-184.
The smooth Whitehead spectrum of a point at odd regular primes
Let be an odd regular prime, and assume that the Lichtenbaum–Quillen conjecture holds for at . Then the –primary homotopy type of the smooth Whitehead spectrum 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 -transfer map . The homotopy groups of are determined in a range of degrees, and the cohomology of is expressed as an -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.
Geom. Topol., Volume 7, Number 1 (2003), 155-184.
Received: 30 November 2001
Revised: 7 February 2003
Accepted: 13 March 2003
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 19D10: Algebraic $K$-theory of spaces
Secondary: 19F27: Étale cohomology, higher regulators, zeta and L-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10] 55P42: Stable homotopy theory, spectra 55Q52: Homotopy groups of special spaces 57R50: Diffeomorphisms 57R80: $h$- and $s$-cobordism
Rognes, John. The smooth Whitehead spectrum of a point at odd regular primes. Geom. Topol. 7 (2003), no. 1, 155--184. doi:10.2140/gt.2003.7.155. https://projecteuclid.org/euclid.gt/1513883095