Volume 9, issue 3 (2005)

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Normalizers of tori

W G Dwyer and C W Wilkerson

Geometry & Topology 9 (2005) 1337–1380

arXiv: math.GR/0508108

Abstract

We determine the groups which can appear as the normalizer of a maximal torus in a connected 2–compact group. The technique depends on using ideas of Tits to give a novel description of the normalizer of the torus in a connected compact Lie group, and then showing that this description can be extended to the 2–compact case.

Keywords
maximal torus, Weyl group, 2–compact group
Mathematical Subject Classification 2000
Primary: 55P35, 55R35
Secondary: 22E10
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Publication
Received: 3 February 2004
Revised: 25 July 2005
Accepted: 6 May 2004
Published: 30 July 2005
Proposed: Haynes Miller
Seconded: Thomas Goodwillie, Ralph Cohen
Authors
W G Dwyer
Department of Mathematics
University of Notre Dame
Notre Dame
Indiana 46556
USA
C W Wilkerson
Department of Mathematics
Purdue University
West Lafayette
Indiana 47907
USA