On the Cohomology Rings of Tree Braid Groups

نویسنده

  • DANIEL FARLEY
چکیده

Let Γ be a 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 [10] 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 < 4. This gives a large number of counterexamples to Ghrist’s conjecture that braid groups of planar graphs are right-angled Artin groups.

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تاریخ انتشار 2008