Skip to main content Accessibility help
×
Home

Generalized Quandle Polynomials

  • Sam Nelson (a1)

Abstract

We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family of link invariants that further generalize the quandle counting invariant.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Generalized Quandle Polynomials
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Generalized Quandle Polynomials
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Generalized Quandle Polynomials
      Available formats
      ×

Copyright

References

Hide All
[1] Carter, J. S., Elhamdadi, M., Graña, M., and Saito, M., Cocycle knot invariants from quandle modules and generalized quandle homology. Osaka J. Math. 42(2005), no. 3, 499541.
[2] Carter, J. S., Jelsovsky, D., Kamada, S., Langford, L., and Saito, M., Quandle cohomology and state-sum invariants of knotted curves and surfaces. Trans. Amer. Math. Soc. 355(2003), no. 10, 39473989. doi:10.1090/S0002-9947-03-03046-0
[3] Eisermann, M.. Quandle coverings and their Galois correspondence. http://arxiv.org/abs/math/0612459.
[4] Fenn, R. and Rourke, C., Racks and links in codimension two. J. Knot Theory Ramifications 1(1992), no. 4, 343406. doi:10.1142/S0218216592000203
[5] Henderson, R., Macedo, T., and Nelson, S., Symbolic computation with finite quandles. J. Symbolic Comput. 41(2006) 811817. doi:10.1016/j.jsc.2006.03.002
[6] Ho, B. and Nelson, S., Matrices and finite quandles. Homology Homotopy Appl. 7(2005), no. 1, 197208.
[7] Joyce, D., A classifying invariant of knots, the knot quandle. J. Pure Appl. Algebra 23(1982), no. 1, 3765. doi:10.1016/0022-4049(82)90077-9
[8] Kauffman, L. H. and Radford, D., Bi-oriented quantum algebras, and a generalized Alexander polynomial for virtual links. In: Diagrammatic morphisms and applications (San Francisco, CA, 2000), Contemp. Math., 318, American Mathematical Society, Providence, RI, 2003, pp. 113140.
[9] Lam, D. and Nelson, S., An isomorphism theorem for Alexander biquandles. Internat. J. Math. 20(2009), no. 1, 97107.
[10] Matveev, S. V., Distributive groupoids in knot theory. (Russian) Mat. Sb. (N.S.) 119(161)(1982), no. 1, 7888, 160.
[11] Nelson, S., A polynomial invariant of finite quandles. J. Algebra Appl. 7(2008), no. 2, 263273. doi:10.1142/S0219498808002801
[12] Nelson, S. and Neumann, W., The 2-generalized knot group determines the knot. Commun. Contemp. Math. 10(2008), suppl. 1, 843847. doi:10.1142/S0219199708003058
[13] Nelson, S. and Vo, J., Matrices and finite biquandles. Homology, Homotopy Appl. 8(2006), no. 2, 5173.
[14] Tuffley, C., Generalised knot groups distinguish the square and granny knots. J. Knot Theory Ramifications 18(2009), no. 8, 11291157. doi:10.1142/S0218216509007385
[15] Zablow, J.. Intersections of curves on surfaces with disk families in handlebodies. J. Knot Theory Ramifications 15(2006), no. 5, 631649. doi:10.1142/S0218216506004671
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Generalized Quandle Polynomials

  • Sam Nelson (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed