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Rotors in Khovanov Homology

Published online by Cambridge University Press:  20 November 2018

Joseph MacColl*
Affiliation:
University of Glagsow, School of Mathematics and Statistics, Glasgow, UK e-mail: [email protected]
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Abstract

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Anstee, Przytycki, and Rolfsen introduced the idea of rotants, pairs of links related by a generalised form of link mutation. We exhibit infinitely many pairs of rotants that can be distinguished by Khovanov homology, but not by the Jones polynomial.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2016

References

[1] The mathematicapackage knottheory. http://katlas.org.Google Scholar
[2] Anstee, R. P., Przytycki, J. H., and Rolfsen, D.. Knot polynomials and generalized mutation. Topology Appl. 32(1989), no. 3, 237249. http://dx.doi.Org/10.1016/0166-8641(89)90031-X Google Scholar
[3] Bar-Natan, D., On Khovanov's categorification of the fones polynomial. Algebr. Geom. Topol. 2(2002), 337370. http://dx.doi.Org/10.2140/agt.2002.2.337 Google Scholar
[4] Bloom, J. M., Odd Khovanov homology is mutation invariant. Math. Res. Lett. 17(2010), no. 1,1-10. http://dx.doi.Org/10.4310/MRL.2010.v1 7.n1 .a1 Google Scholar
[5] Jin, G. T. and Rolfsen, D.. Some remarks on rotors in link theory. Canad. Math. Bull. 34(1991), no. 4, 480484. http://dx.doi.Org/10.4153/CMB-1991-077-1 Google Scholar
[6] Khovanov, Mikhail. A categorification of the Jones polynomial. Duke Math. ., 101(3):359-426, 2000. http://dx.doi.Org/10.121 5/S0012-7094-00-10131-7 Google Scholar
[7] Kronheimer, P. B. and Mrowka, T. S., Khovanov homology is an unknot-detector. Publ. Math. Inst. Hautes Études Sci. 113(2011), 97208.Google Scholar
[8] Rasmussen, J., Knot polynomials and knot homologies. In: Geometry and topology of manifolds, Fields Inst. Commun., 47, American Mathematical Society, Providence, RI, 2005, pp. 261280.Google Scholar
[9] Rolfsen, D., Global mutation of knots. Random knotting and linking (Vancouver, BC, 1993). J. Knot Theory Ramifications 3(1994), no. 3, 407417. http://dx.doi.Org/10.1142/S0218216594000290 Google Scholar
[10] Turner, P., Five lectures on Khovanov homology. 2006. arxiv:math/0606464.Google Scholar
[11] Wehrli, S. M., Mutation invariance of Khovanov homology over ¥2- Quantum Topol. 1(2010), no. 2, 111128. http://dx.doi.Org/10.4171/QT/3 Google Scholar