Representation varieties of RAAGs

2025/12/12 by Bao, Allen, Chakraborty, Anunoy, Duncan, David L. +2
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2512.11235

openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28

Abstract

We investigate the G-representation varieties of right-angled Artin groups (RAAGs) for various Lie groups G. We show these varieties are connected for a large class of such G, including SU(n), Sp(n) and U(n), while they are generally not connected for other large classes, such as SO(n) and Spin(n) for n ≥ 3. When G = SO(3) we determine the number of connected components of the representation variety associated to any RAAG that is also a 3-manifold group.

Citations

• Right-angled Artin groups and a generalized isomorphism problem for\n finitely generated subgroups of mapping class groups

Related

• RAAGs in Ham
• On commensurability of right-angled Artin groups I: RAAGs defined by trees of diameter 4
• Representations of pure symmetric automorphism groups of RAAGs
• On commensurability of some right-angled Artin groups II: RAAGs defined by paths
• An introduction to right-angled Artin groups