The smooth Whitehead spectrum of a point at odd regular primes, by John Rognes

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 S^1-transfer map t : \Sigma C P^\infty \to S. The homotopy of Wh(*) is 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.


John Rognes <rognes@math.uio.no>