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  1. 3 Fundamenta Mathematicae

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  1. 3 Møller J.

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  1. 2 2007

  2. 1 2002

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N-determined p-compact groups

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Møller J.
Fundamenta Mathematicae
|
2002
|
tom 173
|
nr 3
201-300
EN
One of the major problems in the homotopy theory of finite loop spaces is the classification problem for p-compact groups. It has been proposed to use the maximal torus normalizer (which at an odd prime essentially means the Weyl group) as the distinguishing invariant. We show here that the maximal torus normalizer does indeed classify many p-compact groups up to isomorphism when p is an odd prime.
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N-determined 2-compact groups. I

100%
Møller J.
Fundamenta Mathematicae
|
2007
|
tom 195
|
nr 1
11-84
EN
This is the first part of a paper that classifies 2-compact groups. In this first part we formulate a general classification scheme for 2-compact groups in terms of their maximal torus normalizer pairs. We apply this general classification procedure to the simple 2-compact groups of the A-family and show that any simple 2-compact group that is locally isomorphic to PGL(n+1,ℂ) is uniquely N-determined. Thus there are no other 2-compact groups in the A-family than the ones we already know. We also compute the group of automorphisms of any member of the A-family and show that it consists of unstable Adams operations only.
3
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N-determined 2-compact groups. II

100%
Møller J.
Fundamenta Mathematicae
|
2007
|
tom 196
|
nr 1
1-90
EN
This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N-determined and conclude that all connected 2-compact groups are uniquely N-determined. This means that two connected 2-compact groups are isomorphic if their maximal torus normalizer s are isomorphic and that the automorphisms of a connected 2-compact group are determined by their effect on a maximal torus. As an application we confirm the conjecture that any connected 2-compact group is the product of a compact Lie group with copies of the exceptional 2-compact group DI(4).
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