Conjugacy in Garside groups. I: Cyclings, powers and rigidity.

DOI10.4171/GGD/12zbMath1160.20026arXivmath/0605230OpenAlexW1979857659MaRDI QIDQ2472583

Joan S. Birman, Volker Gebhardt, Juan González-Meneses

Publication date: 22 February 2008

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605230

zbMATH Keywords

braid groupsrigidityGarside groupsnormal form theoremsconjugacy search problemconjugacy decision problemiterated cyclingsiterated powersstable ultra summit sets

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Generators, relations, and presentations of groups (20F05) Braid groups; Artin groups (20F36) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (25)

On the centralizer of generic braids ⋮ Noncrossing partitions for periodic braids ⋮ On the genericity of loxodromic actions ⋮ Garside theory and subsurfaces: some examples in braid groups ⋮ Presentations of Dehn quandles ⋮ Recognizing trace graphs of closed braids ⋮ Generalization of the Dehornoy-Lafont order complex to categories: application to exceptional braid groups ⋮ Affine braid groups: a better platform than braid groups for cryptology? ⋮ Small braids with large ultra summit set. ⋮ Reducible braids and Garside theory. ⋮ Fast Nielsen-Thurston classification of braids. ⋮ Conjugacy in Garside groups. III: Periodic braids. ⋮ A Garside-theoretic approach to the reducibility problem in braid groups. ⋮ Conjugacy in Garside groups. II: Structure of the ultra summit set. ⋮ Curve graphs and Garside groups ⋮ The cyclic sliding operation in Garside groups. ⋮ Basic results on braid groups. ⋮ Solving the conjugacy problem in Garside groups by cyclic sliding. ⋮ On the cycling operation in braid groups. ⋮ Towards generating secure keys for braid cryptography ⋮ On parabolic subgroups of Artin-Tits groups of spherical type ⋮ Left-Garside categories, self-distributivity, and braids ⋮ The defect of Bennequin-Eliashberg inequality and Bennequin surfaces ⋮ On dilatation factors of braids on three strands ⋮ A Garside-theoretic analysis of the Burau representations

Cites Work

• Unnamed Item
• Fragments of the word \(\Delta\) in a braid group
• A new approach to the word and conjugacy problems in the braid groups
• Train-tracks for surface homeomorphisms
• An algebraic method for public-key cryptography
• Springer theory in braid groups and the Birman-Ko-Lee monoid.
• The dual braid monoid
• BRAIDS AND THE NIELSEN-THURSTON CLASSIFICATION

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