Abstract
We review recent developments in the theory of Thompson group representations related to knot theory.
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References
C. Adams, Quadruple crossing number of knots and links, emph Math. Proc. Camb. Philos. Soc. 156, 241–253 (2014)
J. Alexander, A lemma on a system of knotted curves. Proc. Natl. Acad. Sci. USA 9, 93–95 (1923)
J. Birman, Braids, Links and Mapping Class Groups. Annals of Mathematics Studies, vol. 82 (Princeton University Press, Princeton, 1975)
J. Birman, On the stable equivalence of Heegaard splittings of plat presentation of links. Canad. J. Math. XXVIII(2), 264–290 (1976)
V. Aiello, R. Conti, V. Jones, The Homflypt polynomial and the oriented Thompson group. Quantum Topol. 9, 461–472 (2018)
J. Belk, Thompson’s group F. Ph.D. Thesis (Cornell University) (2007). arXiv:0708.3609
J.W. Cannon, W.J. Floyd, W.R. Parry, Introductory notes on Richard Thompson’s groups. L’Enseignement Mathématique 42, 215–256 (1996)
J.H. Conway, An enumeration of knots and links, and some of their algebraic properties, in Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) (1970), pp. 329–358
G. Golan, M. Sapir, On Jones’ subgroup of Thompson group F. J. Algebra 470, 122–159 (2017)
R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, 2nd edn. (Addison-Wesley Publishing Company, Boston, 1994)
J.J. Graham, G.I. Lehrer, The representation theory of affine Temperley Lieb algebras. L’Enseignement Mathématique 44, 1–44 (1998)
P. Greenberg, V. Sergiescu, An acyclic extension of the braid group. Comment. Math. Helv. 66, 109–138 (1991)
V. Guba, M. Sapir, Diagram groups. Mem. Am. Math. Soc. 130 (1997)
V. Jones, A no-go theorem for the continuum limit of a periodic quantum spin chain. Commun. Math. Phys. 357, 295–317 (2018)
V.F.R. Jones, Planar Algebras I, preprint, arXiv:math/9909027
V. Jones, On knot invariants related to some statistical mechanical models. Pac. J. Math. 137, 311–334 (1989)
V. Jones Some unitary representations of Thompson’s groups F and T. J. Comb. Algebra 1, 1–44 (2017)
V. Jones, Irreducibility of the wysiwyg represenations of the Thompson group. Preprint (2018)
L. Kauffman, State models and the Jones polynomial. Topology 26, 395–407 (1987)
Y. Ren, From skein theory to presentations for Thompson group (2016), arXiv:1609.04077
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Jones, V.F.R. (2019). On the Construction of Knots and Links from Thompson’s Groups. In: Adams, C., et al. Knots, Low-Dimensional Topology and Applications. KNOTS16 2016. Springer Proceedings in Mathematics & Statistics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-16031-9_3
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DOI: https://doi.org/10.1007/978-3-030-16031-9_3
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