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On braid groups

Sbornik: Mathematics, 2001
Summary: Artin's braid groups are studied from the viewpoint of right-ordered groups. A right order is constructed such that the cone of elements \(\geqslant 1\) is finitely generated as a monoid. The structure of ideals of this cone is determined, and it turns out to be quite specific and impossible for linearly ordered groups.
Dubrovina, T. V., Dubrovin, N. I.
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HOPF-BRAID GROUPS

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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Braid Groups

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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Braids and the Braid Group

2019
This chapter introduces the theory of braids. It explains how a knot diagram can always be expressed as the closure of a braid. Knot equivalence is then transformed into equivalence of closed braids under the braid moves and the Markov moves.
David M. Jackson, Iain Moffatt
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Braid lift representations of Artin's Braid Group

Journal of Knot Theory and Its Ramifications, 2000
We 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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