Geometric structures related to the braided Thompson groups

2018/03/07 by Zaremsky, Matthew C. B.
#20F36 #20F65 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1803.02717

Abstract

In previous work, joint with Bux, Fluch, Marschler and Witzel, we proved that the braided Thompson groups are of type \textrmF_∞. The proof utilized certain contractible cube complexes, which in this paper we prove are CAT(0). We then use this fact to compute the geometric invariants Σ^m(F_\textrmbr) of the pure braided Thompson group F_\textrmbr. Only the first invariant Σ¹(F_\textrmbr) was previously known. A consequence of our computation is that as soon as a subgroup of F_\textrmbr containing the commutator subgroup [F_\textrmbr,F_\textrmbr] is finitely presented, it is automatically of type \textrmF_∞.

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• A short account of why Thompson's group F is of type\n textrmF_\∞
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• The Σ-invariants of Thompson's group F via Morse theory