Non-conjugate braids with the same closure link from density of representations
type: Item
instance of: scholarly article
title: Non-conjugate braids with the same closure link from density of representations
zbMATH Open document ID: 1216.57002
author: Alexander Stoimenow
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2010-11-18T00:00:00Z
review text: Let \(b(L)\) denote the minimal \(n\) such that the link \(L\) is represented by some closed braid from the braid group \(B_n\) on \(n\) strands. The author shows that if \(n>3\), \(L\) is not an \((n-1, k(n-1))\) torus link and \(b(L)<n\), then there exist infinitely many conjugacy classes in \(B_n\) representing \(L\) as a closed braid. Heavy use is made of the Burau and Lawrence-Krammer representations and Lie group theory.
reviewed by: Lee P. Neuwirth
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 22E10
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 11E39
zbMATH DE Number: 5817231
zbMATH Keywords: link
zbMATH Keywords: braid group
zbMATH Keywords: Lie group
zbMATH Keywords: representation
zbMATH Keywords: Hilden subgroup
zbMATH Keywords: conjugacy class
MaRDI profile type: Publication
full work available at URL: j.matpur.2010.08.003
OpenAlex ID: W1994926177
cites work: Theory of braids
cites work: Q4549263
cites work: Braid groups are linear
cites work: Studying Links Via Closed Braids. V: The Unlink
cites work: Studying links via closed braids. III: Classifying links which are closed 3-braids
cites work: Studying links via closed braids. VI: A non-finiteness theorem
cites work: ON THE IMAGE OF THE LAWRENCE–KRAMMER REPRESENTATION
cites work: A presentation for the image of Burau\((4)\otimes Z_2\)
cites work: The maximal subgroups of the classical groups
cites work: A small state sum for knots
cites work: The two-eigenvalue problem and density of Jones representation of braid groups.
cites work: Generators for two subgroups related to the braid group
cites work: THE BRAID GROUP AND OTHER GROUPS
cites work: Hecke algebra representations of braid groups and link polynomials
cites work: Q5734920
cites work: Genera of some closed 4-braids
cites work: Homological representations of the Hecke algebra
cites work: The Burau representation is not faithful for \(n\geq 6\)
cites work: On the generic Krammer representations.
cites work: The Lie algebra of transpositions.
cites work: An irreducible 4-string braid with unknotted closure
cites work: Infinitely many fibred knots having the same Alexander polynomial
cites work: Threading knot diagrams
cites work: On the Braid Index of Alternating Links
cites work: Isotopic Closed Nonconjugate Braids
cites work: Q4126536
cites work: NON-CONJUGATE BRAIDS WHOSE CLOSURES RESULT IN THE SAME KNOT
cites work: The Burau Representation is Unitary
cites work: Coefficients and non-triviality of the Jones polynomial
cites work: On non-conjugate braids with the same closure link
cites work: A presentation for Hilden's subgroup of the braid group
cites work: Quantum groups and subfactors of type B, C, and D
cites work: On Krammer's representation of the braid group.
DOI: 10.1016/J.MATPUR.2010.08.003
description: scientific article; zbMATH DE number 5817231