The classification of 2-compact groups
| dc.creator | Andersen, Kasper K. S. | |
| dc.creator | Grodal, Jesper | |
| dc.date | 2006-11-14 | |
| dc.date | 2007-01-11 | |
| dc.date.accessioned | 2026-07-07T12:54:54Z | |
| dc.date.available | 2026-07-07T12:54:54Z | |
| dc.description | 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. | |
| dc.description | 47 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611437 | |
| dc.identifier | http://arxiv.org/abs/math/0611437 | |
| dc.identifier | J. Amer. Math. Soc. 22 (2009), 387-436 | |
| dc.identifier | doi:10.1090/S0894-0347-08-00623-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224099 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Group Theory | |
| dc.subject | Primary: 55R35; Secondary: 55P35, 55R37 | |
| dc.title | The classification of 2-compact groups | |
| dc.type | text |