## Geometry & Topology

### The smooth Whitehead spectrum of a point at odd regular primes

John Rognes

#### 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.

#### Article information

Source
Geom. Topol., Volume 7, Number 1 (2003), 155-184.

Dates
Revised: 7 February 2003
Accepted: 13 March 2003
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883095

Digital Object Identifier
doi:10.2140/gt.2003.7.155

Mathematical Reviews number (MathSciNet)
MR1988283

Zentralblatt MATH identifier
1130.19300

#### Citation

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

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