N-determined 2-compact groups

TL;DR

This paper develops a classification scheme for 2-compact groups using maximal torus normalizer pairs, demonstrating that many are N-determined and confirming a conjecture by Dwyer and Wilkerson.

Contribution

It introduces a general classification framework for 2-compact groups and proves that all connected and some non-connected groups are N-determined, also computing automorphism groups.

Findings

All connected 2-compact groups are N-determined.

Some non-connected 2-compact groups are N-determined.

The splitting conjecture by Dwyer and Wilkerson is confirmed.

Abstract

We first formulate a general scheme for the classification of 2-compact groups in terms of maximal torus normalizer pairs. Applying this scheme, we show that all connected and some non-connected 2-compact groups are N-determined. We also compute automorphism groups in many cases. As an application we confirm the splitting conjecture formulated by Dwyer and Wilkerson.