On a Generalization of Alexander Polynomial for Long Virtual Knots

Abstract

We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by $\zeta$ meaning an analogy with $\zeta$-polynomial for virtual links. A degree of $\zeta$-polynomial estimates a virtual crossing number. We describe some application of $\zeta$-polynomial for the study of minimal long virtual diagrams with respect number of virtual crossings.

arXiv comment5 pages, 1 figure

References in corpus (1)

• On Alexander-Conway Polynomials for Virtual Knots and Links