Alexander and writhe polynomials for virtual knots

作者：Mellor Blake^*

来源：Journal of Knot Theory and Its Ramifications, 2016, 25(8): 1650050.

DOI：10.1142/S0218216516500504

• Alexander polynomial
• writhe polynomial
• virtual knots
• odd writhe

We give a new interpretation of the Alexander polynomial Delta(0) for virtual knots due to Sawollek [On Alexander-Conway polynomials for virtual knots and Links, preprint (2001), arXiv:math/9912173] and Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications 12 (2003) 987-1000], and use it to show that, for any virtual knot, Delta(0) determines the writhe polynomial of Cheng and Gao [A polynomial invariant of virtual links, J. Knot Theory Ramifications 22(12) (2013), Article ID: 1341002, 33pp.] (equivalently, Kauffman's affine index polynomial [An affine index polynomial invariant of virtual knots, J. Knot Theory Ramifications 22(4) (2013), Article ID: 1340007, 30pp.]). We also use it to define a second-order writhe polynomial, and give some applications.

• 出版日期2016-7