Displaying similar documents to “Braids: generalizations, presentations and algorithmic properties.”

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,...

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...

Virtual braids

Louis H. Kauffman, Sofia Lambropoulou (2004)

Fundamenta Mathematicae

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This paper gives a new method for converting virtual knots and links to virtual braids. Indeed, the braiding method given here is quite general and applies to all the categories in which braiding can be accomplished. This includes the braiding of classical, virtual, flat, welded, unrestricted, and singular knots and links. We also give reduced presentations for the virtual braid group and for the flat virtual braid group (as well as for other categories). These reduced presentations...

Conjugacy for positive permutation braids

Hugh R. Morton, Richard J. Hadji (2005)

Fundamenta Mathematicae

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Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate. ...

A characterization of 2-knots groups.

Francisco González-Acuña (1994)

Revista Matemática Iberoamericana

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A n-knot group is the fundamental group of the complement of an n-sphere smoothly embedded in Sn+2. Artin gave in 1925 ([A]) an algebraic characterization of 1-knot groups. M. Kervaire gave in 1965 ([K]) an algebraic characterization of n-knot groups for n ≥ 3. The problem of characterizing algebraically 2-knot groups has been posed several times (see for example [Su, Problem 4.7]). Ribbon 2-knot groups have been characterized algebraically by Yajima [Y]. ...

Homology of braid groups and their generalizations

Vladimir Vershinin (1998)

Banach Center Publications

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In the paper we give a survey of (co)homologies of braid groups and groups connected with them. Among these groups are pure braid groups and generalized braid groups. We present explicit formulations of some theorems of V. I. Arnold, E. Brieskorn, D. B. Fuks, F. Cohen, V. V. Goryunov and others. The ideas of some proofs are outlined. As an application of (co)homologies of braid groups we study the Thom spectra of these groups.

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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