Results 281 to 290 of about 14,402,713 (324)

The braid group of a necklace

, 2014
We show several geometric and algebraic aspects of a necklace: a link composed with a core circle and a series of (unlinked) circles linked to this core. We first prove that the fundamental group of the configuration space of necklaces (that we will call
P. Bellingeri, Arnaud Bodin
semanticscholar   +1 more source

A kernel of a braid group representation yields a knot with trivial knot polynomials

, 2014
We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus.
Tetsuya Ito
semanticscholar   +1 more source

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
openaire   +1 more source

The 6-strand braid group is CAT(0)

, 2013
We show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes, and the embeddability of their diagonal links into spherical buildings of type A.
Thomas Haettel, Dawid Kielak, Petra Schwer   +2 more
semanticscholar   +1 more source

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
openaire   +1 more source

The pure virtual braid group is quadratic

, 2011
If an augmented algebra $$K$$ over $$\mathbb Q $$ is filtered by powers of its augmentation ideal $$I$$, the associated graded algebra $$gr_I K$$ need not in general be quadratic: although it is generated in degree 1, its relations may not be generated ...
Peter Lee
semanticscholar   +1 more source

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.
openaire   +1 more source

Decomposable braids as subgroups of braid groups

Transactions of the American Mathematical Society, 1975
The group of all decomposable 3 3 -braids is the commutator subgroup of the group I 3 {I_3} of all 3 3 -braids which leave strand positions invariant. The group of all 2 2 -decomposable 4 4 -braids is the commutator subgroup of
openaire   +2 more sources

Braided Coadditive Differential Complexes on Quantized Braided Groups

International Journal of Theoretical Physics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gao, Yajun, Gui, Yuan-Xing
openaire   +2 more sources

Localization of Unitary Braid Group Representations

, 2010
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category.
E. Rowell, Zhenghan Wang
semanticscholar   +1 more source