Algebra Seminar 

16/01/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Kasper Andersen, Centre de Recerca Matemàtica, Barcelona

The classification of $p$-compact groups for odd primes $p$

A central problem in algebraic topology has been to single out the homotopy theoretical properties which characterize compact Lie groups. The right definition of a $p$-local version of a compact Lie group came with Dwyer and Wilkerson who introduced the so called $p$-compact groups and proved that they possess many nice properties. For example a $p$-compact group has a maximal torus, a maximal torus normalizer and a Weyl group.

For odd primes $p$, we give a classification of p-compact groups by proving that they are determined by their maximal torus normalizers. In particular the Weyl group data gives a bijection between connected $p$-compact groups and finite $p$-adic reflection groups.

A number of corollaries follow easily from this classification, for example we give an affirmative answer to the maximal torus conjecture for finite loop spaces up to $\mathbb{Z}[1/2]$-localization.