Displaying similar documents to “The proof of Birman's conjecture on singular braid monoids.”

About presentations of braid groups and their generalizations

V. V. Vershinin (2014)

Banach Center Publications

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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...

Units of the string link monoids

(2014)

Banach Center Publications

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We show that the map obtained by viewing a geometric (i.e. representative) braid as a string link induces an isomorphism of the n-strand braid group onto the group of units of the n-strand string link monoid.

The dual braid monoid

David Bessis (2003)

Annales scientifiques de l'École Normale Supérieure

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The virtual and universal braids

Valerij G. Bardakov (2004)

Fundamenta Mathematicae

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We study the structure of the virtual braid group. It is shown that the virtual braid group is a semi-direct product of the virtual pure braid group and the symmetric group. Also, it is shown that the virtual pure braid group is a semi-direct product of free groups. From these results we obtain a normal form of words in the virtual braid group. We introduce the concept of a universal braid group. This group contains the classical braid group and has as quotients the singular braid group,...

Comultiplication on monoids.

Arkowitz, Martin, Gutierrez, Mauricio (1997)

International Journal of Mathematics and Mathematical Sciences

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The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm

Richard Laver, Sheila Miller (2013)

Open Mathematics

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The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the...