Title: p-compact groups as framed manifolds
author: Tilman Bauer
Address: Department of Mathematics, Rm. 2-492, Massachusetts Institute
of Technology, Cambridge (MA) 02139
E-mail: tilman@mit.edu
We describe a natural way to associate to any p-compact group an
element of the p-local stable stems, which, applied to the p-completion
of a compact Lie group G, coincides with the element represented by
the manifold G with its left-invariant framing. To this end, we
construct a d-dimensional sphere SG with a stable G- action for every
d-dimensional p-compact group G, which generalizes the one-point
compactification of the Lie algebra of a Lie group. The homotopy class
represented by G is then constructed by means of a transfer map
between the Thom spaces of spherical fibrations over BG associated with
SG .