The smooth Whitehead spectrum of a point at odd regular primes

By John Rognes. 2003

49 citations recorded by the source corpus.

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 o, and the torsion homotopy of the remainder equals the torsion homotopy of the ber of the restricted S 1 -transfer map t : C P 1 ! 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 dieomorphisms of highly connected, high dimensional compact smooth manifolds.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9145ef8f02f2e40601d0f07afaeaf6a8372b63e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. T. Goodwillie
2. R. McCarthy
3. Bjørn Ian Dundas

In Geometry and Topology

1. T. Goodwillie
2. R. McCarthy
3. Bjørn Ian Dundas

In Mathematical Physics

1. T. Goodwillie
2. R. McCarthy
3. Bjørn Ian Dundas
4. Jacob Lurie

Citations in the corpus

• The Local Structure of Algebraic K-Theory (2012, background): “Rognes analyzes the cohomology of the Whitehead spectrum in two papers, [242] which gives the 2-primary information and [243] which gives the information at odd regular primes.”