Talk:Burau representation
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And Burau is...?[edit]
As an encyclopedia article, this has a serious flaw: it says nothing about Burau, who s/he is/was, and what is the connection between him/her and the Burau representation. Plclark (talk) 10:58, 10 January 2010 (UTC)
- Good point. I've added a short sentence (and a citation) as a partial answer to this question, but it could probably do with further elaboration. -- Nicholas Jackson (talk) 15:19, 10 January 2010 (UTC)
Alexander formula wrong?[edit]
I think the formula for the Alexander polynomial is off by a normalization: I think it should be multiplied by (t-1)/(t^n-1), where n is the braid index. See, for example, Ohtsuki, Quantum Invariants, Theorem 2.4 (p. 36).
It might be nice to also give some formulas for the reduced / unreduced Burau representations (with matrices). — Preceding unsigned comment added by RobertLipshitz (talk • contribs) 22:39, 15 February 2014 (UTC)
- And with that fix, it's still only true up to a unit in the polynomial ring. --pred (talk) 06:35, 11 March 2014 (UTC)
+++++++++++++++++++++++++++++++ (:+{)} Drwonmug 13:12, 20 July 2018 (UTC)Drwonmug
In a previous post I raised some questions about this entry, which have now been resolved by conversations with experts, and I have no further qualms. However I suggest adding a reference to
Hecke Algebra Representations of Braid Groups and Link Polynomials, V. F. R. Jones, Annals of Mathematics 126 (Sep., 1987), pp. 335-388 Stable URL: http://www.jstor.org/stable/1971403
which contains (in eq 7.4) a formula for det (1 - \beta) in terms of the Conway-Alexander polynomial, which is unambiguously normalized.
— Preceding unsigned comment added by Drwonmug (talk • contribs) 15:31, 10 July 2018 (UTC)
Incorrect Attribution[edit]
Bigelow showed that Burau is not faithful for n = 5, not for n ≥ 5. In fact, in Bigelow's paper cited here, the abstract attributes n ≥ 9 to Moody and n ≥ 6 to Long and Paton. — Preceding unsigned comment added by 2601:2C6:4701:2E00:957E:D574:DDFD:D395 (talk) 21:47, 10 September 2016 (UTC)