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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 braid monoid in Birman-Ko-Lee generators is described as well.
V. V. Vershinin. "About presentations of braid groups and their generalizations." Banach Center Publications 100.1 (2014): 235-271. <http://eudml.org/doc/281659>.
@article{V2014, abstract = {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 braid monoid in Birman-Ko-Lee generators is described as well.}, author = {V. V. Vershinin}, journal = {Banach Center Publications}, keywords = {braid groups; presentations; inverse braid monoids; Artin-Brieskorn groups; singular braid monoids; word problem; conjugacy problem}, language = {eng}, number = {1}, pages = {235-271}, title = {About presentations of braid groups and their generalizations}, url = {http://eudml.org/doc/281659}, volume = {100}, year = {2014}, }
TY - JOUR AU - V. V. Vershinin TI - About presentations of braid groups and their generalizations JO - Banach Center Publications PY - 2014 VL - 100 IS - 1 SP - 235 EP - 271 AB - 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 braid monoid in Birman-Ko-Lee generators is described as well. LA - eng KW - braid groups; presentations; inverse braid monoids; Artin-Brieskorn groups; singular braid monoids; word problem; conjugacy problem UR - http://eudml.org/doc/281659 ER -