The 4-string Braid group $B 4$ has property RD and exponential mesoscopic rank - Mathematics > Group TheoryReport as inadecuate




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Abstract: We prove that the braid group $B 4$ on 4 strings, as well as its centralquotient $B 4-< z>$, have the property RD of Haagerup-Jolissaint. It followsthat the automorphism group $\AutF 2$ of the free group $F 2$ on 2 generatorshas property RD. We also prove that the braid group $B 4$ is a group ofintermediate rank of dimension 3. Namely, we show that both $B 4$ and itscentral quotient have exponential mesoscopic rank, i.e., that they containexponentially many large flat balls which are not included in flats.



Author: Sylvain Barré LMAM, Mikael Pichot

Source: https://arxiv.org/



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