2025/02/14 by An, Byung Hee, Oh, Sangrok
#20F36 #20F65 #20F67 (Primary) 57M60 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2502.10366
In \citeOh22, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an intersection complex, which is a quasi-isometry invariant. In this paper, using the theory of intersection complexes, we classify the class of 2-braid groups over graphs with circumference ≤ 1 up to quasi-isometry. Moreover, we find a sufficient condition when such a graph 2-braid group is quasi-isometric to a right-angled Artin group or not. Finally, by applying the same method, we also find that there is an algorithm to determine whether two 4-braid groups over trees are quasi-isometric or not.