On the cohomology rings of tree braid groups

AbstractLet Γ be a finite connected graph. The (unlabelled) configuration space UCnΓ of n points on Γ is the space of n-element subsets of Γ. The n-strand braid group of Γ, denoted BnΓ, is the fundamental group of UCnΓ.We use the methods and results of [Daniel Farley, Lucas Sabalka, Discrete Morse theory and graph braid groups, Algebr. Geom. Topol. 5 (2005) 1075–1109. Electronic] to get a partial description of the cohomology rings H∗(BnT), where T is a tree. Our results are then used to prove that BnT is a right-angled Artin group if and only if T is linear or n