# Divergence and quasimorphisms of right-angled Artin groups - Mathematics > Group Theory

Divergence and quasimorphisms of right-angled Artin groups - Mathematics > Group Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We give a group theoretic characterization of geodesics with superlineardivergence in the Cayley graph of a right-angled Artin group AG withconnected defining graph G. We use this to determine when two points in anasymptotic cone of AG are separated by a cut-point. As an application, weshow that if G does not decompose as the join of two subgraphs, then AG hasan infinite-dimensional space of non-trivial quasimorphisms. By the work ofBurger and Monod, this leads to a superrigidity theorem for homomorphisms fromlattices into right-angled Artin groups.

Author: ** Jason Behrstock, Ruth Charney**

Source: https://arxiv.org/