The group of parenthesized braids.

DOI10.1016/j.aim.2005.07.012zbMath1160.20027arXivmath/0407097OpenAlexW2027381976MaRDI QIDQ2504374

Patrick Dehornoy

Publication date: 25 September 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407097

zbMATH Keywords

Coxeter relationsbraid groupsCantor setsmapping class groupsgroups of fractionsThompson group \(F\)orderable groupsautomorphisms of free groupsword reversingself-distributive structures

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Sets with a single binary operation (groupoids) (20N02)

Related Items (max. 100)

Diffeomorphism groups of tame Cantor sets and Thompson-like groups ⋮ The braided Thompson's groups are of type \(F_\infty\) ⋮ A new family of infinitely braided Thompson's groups ⋮ Classification of Thompson related groups arising from Jones' technology II ⋮ Orderings of Witzel–Zaremsky–Thompson groups ⋮ A no-go theorem for the continuum limit of a periodic quantum spin chain ⋮ Asymptotically rigid mapping class groups. I: Finiteness properties of braided Thompson's and Houghton's groups ⋮ Divergence function of the braided Thompson group ⋮ Finiteness properties for relatives of braided Higman-Thompson groups ⋮ Skew-braces and \(q\)-braces ⋮ Forest-skein groups II: Construction from homogeneously presented monoids ⋮ A Thompson group for the basilica ⋮ Polynomial Lemniscates and Their Fingerprints: From Geometry to Topology ⋮ Using groups for investigating rewrite systems ⋮ On Belk's classifying space for Thompson's group \(F\) ⋮ The braided Ptolemy-Thompson group is finitely presented. ⋮ The algebra of strand splitting. I. A braided version of Thompson's group V ⋮ Classifying spaces from Ore categories with Garside families ⋮ The braid shelf ⋮ The rotation number integer quantization effect in braid groups ⋮ Big Mapping Class Groups: An Overview ⋮ On the automorphism group of the asymptotic pants complex of an infinite surface of genus zero ⋮ Cryptanalysis of the Shpilrain-Ushakov protocol for Thompson's group ⋮ Asymptotic mapping class groups of closed surfaces punctured along Cantor sets ⋮ Qualgebras and knotted 3-valent graphs ⋮ Garside combinatorics for Thompson's monoid \(F^+\) and a hybrid with the braid monoid \(B_{\infty }^{+}\) ⋮ A prismatic classifying space ⋮ Some aspects of the SD-world ⋮ Higher finiteness properties of braided groups ⋮ A user's guide to cloning systems ⋮ Almost-automorphisms of trees, cloning systems and finiteness properties ⋮ Shrinking braids and left distributive monoid ⋮ Geometric presentations for Thompson's groups. ⋮ FREE AUGMENTED LD-SYSTEMS ⋮ Geometric structures related to the braided Thompson groups

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