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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/







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