Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-31T14:17:33.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotors in Khovanov Homology

Published online by Cambridge University Press:  20 November 2018

Joseph MacColl
Joseph MacColl*
Affiliation:
University of Glagsow, School of Mathematics and Statistics, Glasgow, UK e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

57M2727M25geometric topologyknot theoryrotantskhovanov homologyjones polynomial
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016 , pp. 159 - 169
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, 237–249. 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), 337–370. 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, 480–484. 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), 97–208.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. 261–280.Google Scholar
[9] Rolfsen, D., Global mutation of knots. Random knotting and linking (Vancouver, BC, 1993). J. Knot Theory Ramifications 3(1994), no. 3, 407–417. 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, 111–128. http://dx.doi.Org/10.4171/QT/3 Google Scholar