Algebraic & Geometric Topology

Representations of surface groups and right-angled Artin groups in higher rank

Stephen Wang

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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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1099-1117.

Dates
Received: 2 February 2007
Revised: 8 June 2007
Accepted: 12 June 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796716

Digital Object Identifier
doi:10.2140/agt.2007.7.1099

Mathematical Reviews number (MathSciNet)
MR2336251

Zentralblatt MATH identifier
1133.20024

Subjects
Primary: 20F36: Braid groups; Artin groups
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
Artin groups Lie groups

Citation

Wang, Stephen. Representations of surface groups and right-angled Artin groups in higher rank. Algebr. Geom. Topol. 7 (2007), no. 2, 1099--1117. doi:10.2140/agt.2007.7.1099. https://projecteuclid.org/euclid.agt/1513796716


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