Divergence and quasimorphisms of right-angled Artin groups

2010/01/20 by Jason Behrstock, Behrstock, Jason, Ruth Charney +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1001.3587

openalex publication_date 2010/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A(G) with connected defining graph G. We use this to determine when two points in an asymptotic cone of A(G) are separated by a cut-point. As an application, we show that if G does not decompose as the join of two subgraphs, then A(G) has an infinite-dimensional space of non-trivial quasimorphisms. By the work of Burger and Monod, this leads to a superrigidity theorem for homomorphisms from lattices into right-angled Artin groups.

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