Basic results on braid groups
By Juan González-Meneses. 2010
48 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/26bfb5c5818e0b472b761a73a394ba080fda7256
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A journey through loop braid groups (2016, background): “Then the group PMCG(D2, P ) is isomorphic to Pn, the pure braid group on n strands, and MCG(D2, P ) is isomorphic to Bn, the braid group on n strands, as defined, for example, in [27] or [36, Chapter 1.”