The classification of 2compact groups
(2009) In Journal of the American Mathematical Society 22(2). p.387436 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... (More)  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 by incorporating the theory of root data over the padic integers, as developed by DwyerWilkerson and the authors. Furthermore we devise a different way of dealing with the rigidification problem by utilizing obstruction groups calculated by JackowskiMcClureOliver in the early 1990s. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3412526
 author
 Andersen, Kasper ^{LU} and Grodal, Jesper
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of the American Mathematical Society
 volume
 22
 issue
 2
 pages
 387  436
 publisher
 American Mathematical Society (AMS)
 external identifiers

 scopus:77950582963
 ISSN
 08940347
 DOI
 10.1090/S0894034708006231
 language
 English
 LU publication?
 no
 id
 3060e3475d2846eda32917800df38bc9 (old id 3412526)
 alternative location
 http://www.ams.org/journals/jams/20092202/S0894034708006231/
 date added to LUP
 20130425 16:40:07
 date last changed
 20180107 06:17:01
@article{3060e3475d2846eda32917800df38bc9, abstract = {We prove that any connected 2compact group is classified by its<br/><br> 2adic root datum, and in particular the exotic 2compact group<br/><br> 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 by incorporating the theory of root data over the padic integers, as developed by DwyerWilkerson and the authors. Furthermore we devise a different way of dealing with the rigidification problem by utilizing obstruction groups calculated by JackowskiMcClureOliver in the early 1990s.}, author = {Andersen, Kasper and Grodal, Jesper}, issn = {08940347}, language = {eng}, number = {2}, pages = {387436}, publisher = {American Mathematical Society (AMS)}, series = {Journal of the American Mathematical Society}, title = {The classification of 2compact groups}, url = {http://dx.doi.org/10.1090/S0894034708006231}, volume = {22}, year = {2009}, }