The infimum, supremum, and geodesic length of a braid conjugacy class.

DOI10.1006/aima.2001.2010zbMath1063.20039arXivmath/0003125OpenAlexW2030857786MaRDI QIDQ5957497

Joan S. Birman, Sang Jin Lee, Ki Hyoung Ko

Publication date: 2001

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

Full work available at URL: https://arxiv.org/abs/math/0003125

zbMATH Keywords

conjugacy classesbraid groupsword lengthsbraid indicesconjugacy problemgeodesic lengthspolynomial-time algorithms

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Conjugacy classes for groups (20E45) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (20)

Conjugacy languages in groups ⋮ Computation of centralizers in braid groups and Garside groups. ⋮ Positivities of Knots and Links and the Defect of Bennequin Inequality ⋮ Garside groups are strongly translation discrete. ⋮ The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient \(B_n/[P_{n},P_{n}\)] ⋮ FAST ALGORITHMIC NIELSEN–THURSTON CLASSIFICATION OF FOUR-STRAND BRAIDS ⋮ Interval groups related to finite Coxeter groups Part II ⋮ Conjugacy problem for braid groups and Garside groups. ⋮ Conjugacy search in braid groups. From a braid-based cryptogrphy point of view ⋮ Fast Nielsen-Thurston classification of braids. ⋮ Algorithmic recognition of quasipositive braids of algebraic length two. ⋮ Conjugacy in Garside groups. III: Periodic braids. ⋮ Conjugacy in Garside groups. II: Structure of the ultra summit set. ⋮ The cyclic sliding operation in Garside groups. ⋮ Braids, their Properties and Generalizations ⋮ Towards generating secure keys for braid cryptography ⋮ A New Approach to Extracting Roots in Garside Groups ⋮ On parabolic subgroups of Artin-Tits groups of spherical type ⋮ A FAMILY OF PSEUDO-ANOSOV BRAIDS WHOSE SUPER-SUMMIT SETS GROW EXPONENTIALLY ⋮ A new approach to the conjugacy problem in Garside groups.

Cites Work

• A new approach to the word and conjugacy problems in the braid groups
• Geodesic automation and growth functions for Artin groups of finite type
• Band-generator presentation for the 4-braid group
• THE GENUS OF CLOSED 3-BRAIDS
• ALGORITHMS FOR POSITIVE BRAIDS
• THE BRAID GROUP AND OTHER GROUPS
• The braid group \(B_4\) is linear
• Unnamed Item

This page was built for publication: The infimum, supremum, and geodesic length of a braid conjugacy class.