Taylor series coefficients of the HP-polynomial as an invariant for links in the solid torus

Authors

K. Bataineh, Jordan University of Science and Technology, Jordan and University of Bahrain, Bahrain

Author Country (or Countries)

Bahrain

Abstract

We show that the coe±cients of a reformulation of a Taylor series expansion of the Hoste and Pryzyticki polynomial are Vassiliev invariants. We also show that many other reformulations of the Taylor series expansion have coe±cients that are Vassiliev invariants. We charecterize the ¯rst two coe±cients b1 0(t) and bL 1 (t) for one of these expan- sions. Moreover, the second coe±cient bL 1 (t); which is a type-one Vassiliev invariant, is given two explicit computational formulas, which are easy to calculate. bL 1 (t) is used to give a lower bound for the crossing number of a knot of zero winding number in the solid torus.

Suggested Reviewers

N/A

Recommended Citation

Bataineh, K. (2013) "Taylor series coefficients of the HP-polynomial as an invariant for links in the solid torus," Applied Mathematics & Information Sciences: Vol. 07: Iss. 1, Article 25.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/25