Results 21 to 30 of about 285 (147)
The Interplay between Linear Representations of the Braid Group
International Journal of Mathematics and Mathematical Sciences, 2007 We consider Wada's representation as a twisted version of the standard action of the braid group, Bn, on the free group with n generators. Constructing a free group, Gnm, of rank nm, we compose Cohen's map Bn→Bnm and the embedding Bnm→Aut(Gnm) via Wada's
Mohammad N. Abdulrahim, Nibal H. Kassem
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Multi-parameter Burau representations
Tamkang Journal of Mathematics, 2013 We consider the multi-parameter representation of Artin's braid group introduced by D. D. Long and J. P. Tian, namely $\alpha: B_{n}\rightarrow GL_{m}(C)$, where $m=n!n$ . First, we show that there exists a complex specialization of the multi-parameter representation that does not arise from any Hecke algebra. Second, we find conditions under which the
Al-Tahan, Madline +2 more
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ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION [PDF]
Journal of Knot Theory and Its Ramifications, 2001 Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. The group of virtual braids on n strings VBn and its Burau representation to GLnℤ[t,t-1] also can be considered. The homological properties of the series of groups VBn and its Burau representation are studied.
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The Burau representation is not faithful forn= 5 [PDF]
Geometry & Topology, 1999 8 pages.
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On the subgroup of $B_4$ that contains the kernel of Burau representation
, 2021 It is known that there are braids $α$ and $β$ in the braid group $B_4$, such that the group $\langle α, β\rangle$ is a fee subgroup \cite{7}, which contains the kernel $K$ of the Burau map $ρ_4 : B_4 \to G L\left(3, \mathbb{Z}[t,t^{-1}]\right)$ \cite{6}, \cite{4}.
Beridze, Anzor, Davitadze, Levan
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Classical link invariants and the Burau representation [PDF]
Pacific Journal of Mathematics, 1990 The author demonstrates an intriguing connection between the Burau representation of an element of the braid group and the Alexander module of the link obtained by closing the braid. In the same spirit, a connection is made between a Hermitian form on the torsion submodule of the Alexander module and the Blanchfield pairing.
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The Burau representations of loop braid groups
Comptes Rendus. Mathématique, 2022 We give a simple topological construction of the Burau representations of the loop braid groups. There are four versions: defined either on the non-extended or extended loop braid groups, and in each case there is an unreduced and a reduced version. Three are not surprising, and one could easily guess the correct matrices to assign to generators.
Martin Palmer, Arthur Soulié
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On the Burau representation modulo a small prime [PDF]
Geometry & Topology Monographs, 1998 12 pages.
Cooper, Daryl, Long, Darren D.
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Toward the group completion of the Burau representation
Transactions of the American Mathematical Society, 2022 Following Boardman-Vogt, McDuff, Segal, and others, we construct a monoidal topological groupoid or space of finite subsets of the plane, and interpret the Burau representation of knot theory as a topological quantum field theory defined on it.
Morava, Jack, Rolfsen, Dale
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Observed Periodicity Related to the Four-Strand Burau Representation [PDF]
Experimental Mathematics, 2017 A long-standing open problem is to determine for which values of n the Burau representation Psi_n of the braid group B_n is faithful. Following work of Moody, Long-Paton, and Bigelow, the remaining open case is n = 4. One criterion states that Psi_n is unfaithful if and only if there exists a pair of arcs in the n-punctured disk D_n such that a certain
Neil J. Fullarton, Richard Shadrach
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