The classification of p-compact groups for p odd

Details The classification of p-compact groups for p odd The classification of p-compact groups for p odd

2003-02-27

arxiv.org/abs/math/0302346v5

Annals of Math. 167 (2008), 95--210

Mathematics

Algebraic Topology

92 pages. Final version. To appear in Ann. of Math

Scientific paper

A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem.

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