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The classification of p-compact groups for p odd

In English

Författare

Summary, in English

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 for p odd.

Publiceringsår

2008

Språk

Engelska

Sidor

95-210

Publikation/Tidskrift/Serie

Annals of Mathematics

Volym

167

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

Annals of Mathematics

Ämne

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0003-486X