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ON NORMALIZERS IN THE BRAID GROUP
Mathematics of the USSR-Sbornik, 1971Let be the normalizer of an element in the braid broup . It is shown that is finitely generated, and a method for finding generators for is indicated. Bibliography: 4 items.
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Algebra and Logic, 2003
\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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Russian Academy of Sciences. Sbornik Mathematics, 1993
Let \(V\) be a set of (finite) words in an alphabet of variables ranging over elements of a group \(G\). The subgroup \(V(G)\) of the group \(G\) generated by all values of words from \(V\) is called the verbal subgroup defined by the set \(V\). The width of the subgroup \(V(G)\) is defined to be the minimal number \(m \in \mathbb{N} \cup \{+\infty\}\)
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Let \(V\) be a set of (finite) words in an alphabet of variables ranging over elements of a group \(G\). The subgroup \(V(G)\) of the group \(G\) generated by all values of words from \(V\) is called the verbal subgroup defined by the set \(V\). The width of the subgroup \(V(G)\) is defined to be the minimal number \(m \in \mathbb{N} \cup \{+\infty\}\)
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Journal of Knot Theory and Its Ramifications, 1998
In this note we define the Hopf-braid group, a group that is directly related to the group of motions of n mutually distinct lines through the origin in [Formula: see text], which is better known as the braid group of the two-sphere. It is also related to the motion group of the Hopf link in the three-sphere.
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In this note we define the Hopf-braid group, a group that is directly related to the group of motions of n mutually distinct lines through the origin in [Formula: see text], which is better known as the braid group of the two-sphere. It is also related to the motion group of the Hopf link in the three-sphere.
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The Annals of Mathematics, 1947
In his paper 'Theorie der Z6pfe' E. Artin' presented a theory of braids based on a study of their projections on a two-dimensional plane. In the projection each strand of a braid appears as a line, vertical in general, but at certain levels two neighboring strands interchange position, one strand crossing in front of the other one.
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In his paper 'Theorie der Z6pfe' E. Artin' presented a theory of braids based on a study of their projections on a two-dimensional plane. In the projection each strand of a braid appears as a line, vertical in general, but at certain levels two neighboring strands interchange position, one strand crossing in front of the other one.
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Braid lift representations of Artin's Braid Group
Journal of Knot Theory and Its Ramifications, 2000We recast the braid-lift representation of Contantinescu, Lüdde and Toppan in the language of B-type braid theory. Composing with finite dimensional representations of these braid groups we obtain various sequences of finite dimensional multi-parameter representations.
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1974
The terms “braid” and “braid groups” were coined by Artin, 1925. In his paper, an n-braid appears as a specific topological object. We consider two parallel planes in euclidean 3-space which we call respectively the upper and the lower frame. We choose n distinct points U v (v = 1, ..., n) in the upper frame and denote their orthogonal projections onto
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The terms “braid” and “braid groups” were coined by Artin, 1925. In his paper, an n-braid appears as a specific topological object. We consider two parallel planes in euclidean 3-space which we call respectively the upper and the lower frame. We choose n distinct points U v (v = 1, ..., n) in the upper frame and denote their orthogonal projections onto
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2017
This chapter introduces the reader to Artin's classical braid groups Bₙ. The group Bₙ is isomorphic to the mapping class group of a disk with n marked points. Since disks are planar, the braid groups lend themselves to special pictorial representations.
Benson Farb, Dan Margalit
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This chapter introduces the reader to Artin's classical braid groups Bₙ. The group Bₙ is isomorphic to the mapping class group of a disk with n marked points. Since disks are planar, the braid groups lend themselves to special pictorial representations.
Benson Farb, Dan Margalit
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Effective Parameters on Fabrication and Modification of Braid Hollow Fiber Membranes: A Review
Membranes, 2021Hamed Karkhanechi +2 more
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