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About presentations of braid groups and their generalizations

V. V. Vershinin (2014)

Banach Center Publications

In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation for generalizations of braids. Namely, we consider presentations with small number of generators, Sergiescu graph-presentations and Birman-Ko-Lee presentation. The work of V.~V.~Chaynikov on the word and conjugacy problems for the singular...

Actions of finitely generated groups on -trees

Vincent Guirardel (2008)

Annales de l’institut Fourier

We study actions of finitely generated groups on -trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing together actions of simple types: actions on simplicial trees, actions on lines, and actions coming from measured foliations on 2 -orbifolds. This extends results by Sela and Rips-Sela. However, their results are misstated, and we give a counterexample to their statements.The...

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