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Basic results on braid groups. (Resultats basiques dans les groupes de tresses.) (English. French summary) Zbl 1264.20035
Summary: 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.

MSC:
20F36 Braid groups; Artin groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
Software:
Magma; CHEVIE
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References:
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