Abstract
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups and are quasi-isometric, then is a (nice) subgroup of and vice-versa. We show that the conjecture holds for all known cases of quasi-isometric classification of partially commutative groups, namely for the classes of –trees and atomic graphs. As in the classical Mostow rigidity theory for irreducible lattices, we relate the quasi-isometric rigidity of the class of atomic partially commutative groups with the algebraic rigidity, that is, with the co-Hopfian property of their –completions.
Citation
Montserrat Casals-Ruiz. "Embeddability and quasi-isometric classification of partially commutative groups." Algebr. Geom. Topol. 16 (1) 597 - 620, 2016. https://doi.org/10.2140/agt.2016.16.597
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