Volume 7, issue 2 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Representations of surface groups and right-angled Artin groups in higher rank

Stephen Wang

Algebraic & Geometric Topology 7 (2007) 1099–1117

arXiv: math.GR/0701493

Abstract

We give concrete constructions of discrete and faithful representations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we find a general criterion for when discrete and faithful representations exist, and show that the criterion is satisfied in particular cases. There are direct applications towards constructing representations of surface groups into higher-rank Lie groups, and, in particular, into lattices in higher-rank Lie groups.

Keywords
Artin groups, Lie groups
Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 53C35
References
Publication
Received: 2 February 2007
Revised: 8 June 2007
Accepted: 12 June 2007
Published: 2 August 2007
Authors
Stephen Wang
Department of Mathematics
Haverford College
Haverford PA 19104
USA
http://www.haverford.edu/math/swang/