DOES THE JONES POLYNOMIAL DETECT THE UNKNOT?
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Publication:4549828
DOI10.1142/S0218216502001779zbMath1003.57017arXivmath/0012086WikidataQ56003624 ScholiaQ56003624MaRDI QIDQ4549828
Publication date: 27 January 2003
Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0012086
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Related Items (14)
A free subgroup in the image of the 4-strand Burau representation ⋮ Representations of small braid groups in Temperley-Lieb algebra ⋮ An algorithmic method to compute plat slide moves in 3-manifolds of Heegaard genus two ⋮ The Lawrence-Krammer-Bigelow representations of the braid groups via \(U_q(\mathfrak{sl}_2)\). ⋮ Parity in knot theory and graph-links ⋮ Verification of the Jones unknot conjecture up to 22 crossings ⋮ Random knots using Chebyshev billiard table diagrams ⋮ A new proof of the faithfulness of the Temperley–Lieb representation of B3 ⋮ Reading the dual Garside length of braids from homological and quantum representations. ⋮ Observed Periodicity Related to the Four-Strand Burau Representation ⋮ Coefficients and non-triviality of the Jones polynomial ⋮ Forks, noodles and the Burau representation for \(n = 4\) ⋮ A kernel of a braid group representation yields a knot with trivial knot polynomials ⋮ A Garside-theoretic analysis of the Burau representations
Cites Work
- Hecke algebra representations of braid groups and link polynomials
- Knot polynomials and generalized mutation
- The Burau representation is not faithful for \(n=5\)
- The Burau representation is not faithful for \(n\geq 6\)
- Does the Jones Polynomial Detect Unknottedness?
- Braid groups are linear
- The braid group \(B_4\) is linear
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