Results 1 
2 of
2
The classification of 2compact groups
"... Abstract. We prove that any connected 2compact group is classified by its 2adic root datum, and in particular the exotic 2compact group DI(4), constructed by DwyerWilkerson, is the only simple 2compact group not arising as the 2completion of a compact connected Lie group. Combined with our ear ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
(Show Context)
Abstract. We prove that any connected 2compact group is classified by its 2adic root datum, and in particular the exotic 2compact group DI(4), constructed by DwyerWilkerson, is the only simple 2compact group not arising as the 2completion of a compact connected Lie group. Combined with our earlier work with Møller and Viruel for p odd, this establishes the full classification of pcompact groups, stating that, up to isomorphism, there is a onetoone correspondence between connected pcompact groups and root data over the padic integers. As a consequence we prove the maximal torus conjecture, giving a onetoone 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 AndersenGrodalMøllerViruel methods to incorporate the theory of root data over the padic integers, as developed by DwyerWilkerson and the authors, and we show that certain occurring obstructions vanish, by relating them to obstruction groups calculated by JackowskiMcClureOliver in the early 1990s. 1.
Ndetermined 2compact groups
, 2005
"... Key words and phrases. Classification of pcompact groups at the prime p = 2, ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Key words and phrases. Classification of pcompact groups at the prime p = 2,