The 4-string braid group has property RD and exponential mesoscopic rank
Bulletin de la Société Mathématique de France (2011)
- Volume: 139, Issue: 4, page 479-502
- ISSN: 0037-9484
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topBarré, Sylvain, and Pichot, Mikaël. "The 4-string braid group $B_4$ has property RD and exponential mesoscopic rank." Bulletin de la Société Mathématique de France 139.4 (2011): 479-502. <http://eudml.org/doc/272640>.
@article{Barré2011,
abstract = {We prove that the braid group $B_4$ on 4 strings, its central quotient $B_4/\langle z\rangle $, and the automorphism group $\operatorname\{Aut\}(F_2)$ of the free group $F_2$ on 2 generators, have the property RD of Haagerup–Jolissaint.
We also prove that the braid group $B_4$ is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.},
author = {Barré, Sylvain, Pichot, Mikaël},
journal = {Bulletin de la Société Mathématique de France},
keywords = {braid groups; property RD; CAT(0) spaces},
language = {eng},
number = {4},
pages = {479-502},
publisher = {Société mathématique de France},
title = {The 4-string braid group $B_4$ has property RD and exponential mesoscopic rank},
url = {http://eudml.org/doc/272640},
volume = {139},
year = {2011},
}
TY - JOUR
AU - Barré, Sylvain
AU - Pichot, Mikaël
TI - The 4-string braid group $B_4$ has property RD and exponential mesoscopic rank
JO - Bulletin de la Société Mathématique de France
PY - 2011
PB - Société mathématique de France
VL - 139
IS - 4
SP - 479
EP - 502
AB - We prove that the braid group $B_4$ on 4 strings, its central quotient $B_4/\langle z\rangle $, and the automorphism group $\operatorname{Aut}(F_2)$ of the free group $F_2$ on 2 generators, have the property RD of Haagerup–Jolissaint.
We also prove that the braid group $B_4$ is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.
LA - eng
KW - braid groups; property RD; CAT(0) spaces
UR - http://eudml.org/doc/272640
ER -
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