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arXiv · 0809.0645

The 4-string Braid group $B_4$ has property RD and exponential mesoscopic rank

Sylvain Barré·Mikael Pichot
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Abstract

We prove that the braid group $B_4$ on 4 strings, as well as its central quotient $B_4/< z>$, have the property RD of Haagerup-Jolissaint. It follows that the automorphism group $\Aut(F_2)$ of the free group $F_2$ on 2 generators has property RD. We also prove that the braid group $B_4$ is a group of intermediate rank (of dimension 3). Namely, we show that both $B_4$ and its central quotient have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.

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Sylvain Barré, Mikael Pichot. 2009-02-03. The 4-string Braid group $B_4$ has property RD and exponential mesoscopic rank. https://arxiv.org/abs/0809.0645

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