Webends of some braid b. The Alexander polynomial A(K) was defined in terms of a certain matrix A of relations. In 1-926, Alexander found that A(K) does not uniquely determine the knot K [1]. Subsequently, Burau wrote down, for each braid b, a matrix of Alexander relations of the form A(b) - 1 for the associated knot or link, such that the WebDOI: 10.5539/JMR.V8N1P5 Corpus ID: 55319379; Attacks on the Faithfulness of the Burau Representation of the Braid Group $B_4$ @article{Chreif2016AttacksOT, title ...
On the subgroup of $B_4$ that contains the kernel of Burau representation
WebSubsequently, Burau wrote down, for each braid b, a matrix of Alexander relations of the form A(b) - 1 for the associated knot or link, such that the matrix of a composite bb' satisfies A(bb') = A(b)A(b'). For generic values of the variable, Burau's representation (modulo a line) is Zariski dense, so its exterior powers are distinct irreducible ... WebThis paper introduces braid groups, describes the problem in ways that make it accessible to readers with a minimal background, reviews the literature, and makes a contribution that … dunwoody cobbler shoe repair
On the Burau representation of B4 - ResearchGate
WebBurau. Methods for finding kernel elements of the B_4 Burau representation, or helping to show that no non-trivial elements of the kernel exist.. Background. Here, we follow the lead from Bigelow and consider a particular family of pairs of curves in the four-punctured disc. We follow more or less the same prescription as in Bigelow's C implementation currently … Web22 de set. de 2024 · The Burau representation is a natural action of the braid group B n on the free Z[t; t 1 ]-module of rank n 1. It is a longstanding open problem to determine for which values of n this ... Webpartial answer to the problem of identifying the image of the Burau representation and provides a tool for attacking the question of whether or not the Burau representation is faithful. In [2, problem 14, p. 217], Birman asked for a characterization of the image of the Burau representation,B: Bn -->GLn-I(Z[t, t-1]) of the braid group Bn. dunwoody coffee shops