The 4-string Braid group B 4 has property RD and exponential mesoscopic rank
نویسندگان
چکیده
We prove that the braid group B4 on 4 strings, as well as its central quotient B4/〈z〉, have the property RD of Haagerup–Jolissaint. It follows that the automorphism group Aut(F2) of the free group F2 on 2 generators has property RD. We also prove that the braid group B4 is a group of intermediate rank (of dimension 3). Namely, we show that both B4 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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