A quasi-isometry invariant and thickness bounds for right-angled Coxeter groups

  • Ivan Levcovitz

    Technion - Israel Institute of Technology, Haifa, Israel
A quasi-isometry invariant and thickness bounds for right-angled Coxeter groups cover
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Abstract

We introduce a new quasi-isometry invariant of 2-dimensional right-angled Coxeter groups, the hypergraph index, that partitions these groups into infinitely many quasi-isometry classes, each containing infinitely many groups. Furthermore, the hypergraph index of any right-angled Coxeter group can be directly computed from the group’s defining graph. The hypergraph index yields an upper bound for a right-angled Coxeter group’s order of thickness, order of algebraic thickness and divergence function. Finally, given an integer , we give examples of right-angled Coxeter groups which are thick of order , yet are algebraically thick of order strictly larger than n, answering a question of Behrstock-Druţu-Mosher.

Cite this article

Ivan Levcovitz, A quasi-isometry invariant and thickness bounds for right-angled Coxeter groups. Groups Geom. Dyn. 13 (2019), no. 1, pp. 349–378

DOI 10.4171/GGD/490