Basic results on braid groups

Juan González-Meneses[1]

  • [1] Departamento de Álgebra Facultad de Matemáticas Universidad de Sevilla Apdo. 1160 41080 - Sevilla SPAIN

Annales mathématiques Blaise Pascal (2011)

  • Volume: 18, Issue: 1, page 15-59
  • ISSN: 1259-1734

Abstract

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These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some solutions of the word and conjugacy problems, and that roots of a braid are always conjugate. We also describe the centralizer of a given braid. Most proofs are classical ones, using modern terminology. I have chosen those which I find simpler or more beautiful.

How to cite

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González-Meneses, Juan. "Basic results on braid groups." Annales mathématiques Blaise Pascal 18.1 (2011): 15-59. <http://eudml.org/doc/219712>.

@article{González2011,
abstract = {These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some solutions of the word and conjugacy problems, and that roots of a braid are always conjugate. We also describe the centralizer of a given braid. Most proofs are classical ones, using modern terminology. I have chosen those which I find simpler or more beautiful.},
affiliation = {Departamento de Álgebra Facultad de Matemáticas Universidad de Sevilla Apdo. 1160 41080 - Sevilla SPAIN},
author = {González-Meneses, Juan},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Braids; torsion-free; presentation; Garside; Nielsen-Thurston theory; braid groups; torsion freeness; Dehornoy theorem; orderability; Artin presentations; word problem; conjugacy problem; linearity; centralizers; roots},
language = {eng},
month = {1},
number = {1},
pages = {15-59},
publisher = {Annales mathématiques Blaise Pascal},
title = {Basic results on braid groups},
url = {http://eudml.org/doc/219712},
volume = {18},
year = {2011},
}

TY - JOUR
AU - González-Meneses, Juan
TI - Basic results on braid groups
JO - Annales mathématiques Blaise Pascal
DA - 2011/1//
PB - Annales mathématiques Blaise Pascal
VL - 18
IS - 1
SP - 15
EP - 59
AB - These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some solutions of the word and conjugacy problems, and that roots of a braid are always conjugate. We also describe the centralizer of a given braid. Most proofs are classical ones, using modern terminology. I have chosen those which I find simpler or more beautiful.
LA - eng
KW - Braids; torsion-free; presentation; Garside; Nielsen-Thurston theory; braid groups; torsion freeness; Dehornoy theorem; orderability; Artin presentations; word problem; conjugacy problem; linearity; centralizers; roots
UR - http://eudml.org/doc/219712
ER -

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