The group of parenthesized braids

dc.creatorDehornoy, Patrick
dc.date2004-07-07
dc.date2005-06-27
dc.date.accessioned2026-07-07T06:31:43Z
dc.date.available2026-07-07T06:31:43Z
dc.descriptionWe investigate a group $B\_\bullet$ that includes Artin's braid group $B\_\infty$ and Thompson's group $F$. The elements of $B\_\bullet$ are represented by braids diagrams in which the distances between the strands are not uniform and, besides the usual crossing generators, new rescaling operators shrink or strech the distances between the strands. We prove that $B\_\bullet$ is a group of fractions, that it is orderable, admits a non-trivial self-distributive structure, i.e., one involving the law $x(yz)=(xy)(xz)$, embeds in the mapping class group of a sphere with a Cantor set of punctures, and that Artin's representation of $B\_\infty$ into the automorphisms of a free group extends to $B\_\bullet$.
dc.identifierhttps://arxiv.org/abs/math/0407097
dc.identifierhttp://arxiv.org/abs/math/0407097
dc.identifierAdvances in Mathematics 205 (2006) 354-409
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98691
dc.subjectGroup Theory
dc.subjectMSC 20F36, 20N02, 57M25, 57S05
dc.titleThe group of parenthesized braids
dc.typetext

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