Volume 12, issue 2 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Normalizers of parabolic subgroups of Coxeter groups

Daniel Allcock

Algebraic & Geometric Topology 12 (2012) 1137–1143
Abstract

We improve a bound of Borcherds on the virtual cohomological dimension of the nonreflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink’s result that the nonreflection part of a reflection centralizer is free. Namely, the nonreflection part of the normalizer of parabolic subgroup of type D5 or Amodd is either free or has a free subgroup of index 2.

Keywords
Coxeter group, parabolic subgroup, nonreflection part
Mathematical Subject Classification 2010
Primary: 20F55
References
Publication
Received: 13 September 2011
Accepted: 18 January 2012
Published: 22 May 2012
Authors
Daniel Allcock
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin TX 78712
USA
http://www.math.utexas.edu/~allcock