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N-determined 2-compact groups. I

Jesper M. Møller (2007)

Fundamenta Mathematicae

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...

N-determined 2-compact groups. II

Jesper M. Møller (2007)

Fundamenta Mathematicae

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...

Nilpotency of self homotopy equivalences with coefficients

Maxence Cuvilliez, Aniceto Murillo, Antonio Viruel (2011)

Annales de l’institut Fourier

In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.

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