The classification of 2-compact groups
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
We prove that any connected 2-compact group is classified by its 2-adic root datum, and in particular the exotic 2-compact group DI(4), constructed by Dwyer-Wilkerson, is the only simple 2-compact group not arising as the 2-completion of a compact connected Lie group. Combined with our earlier work with Moeller and Viruel for p odd, this establishes the full classification of p-compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected p-compact groups and root data over the p-adic integers. As a consequence we prove the maximal torus conjecture, giving a one-to-one correspondence between compact Lie groups and finite loop spaces admitting a maximal torus. Our proof is a general induction on the dimension of the group, which works for all primes. It refines the Andersen-Grodal-Moeller-Viruel methods to incorporate the theory of root data over the p-adic integers, as developed by Dwyer-Wilkerson and the authors, and we show that certain occurring obstructions vanish, by relating them to obstruction groups calculated by Jackowski-McClure-Oliver in the early 1990s.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Journal of the American Mathematical Society |
Vol/bind | 22 |
Udgave nummer | 2 |
Sider (fra-til) | 387-436 |
Antal sider | 50 |
ISSN | 0894-0347 |
DOI | |
Status | Udgivet - 2009 |
Bibliografisk note
Paper id:: 10.1090/S0894-0347-08-00623-1
ID: 11483385