On a Generalization of Alexander Polynomial for Long Virtual Knots

Details On a Generalization of Alexander Polynomial for Long Virtual Knots On a Generalization of Alexander Polynomial for Long Virtual Knots

2009-06-23

arxiv.org/abs/0906.4245v1

Mathematics

Geometric Topology

5 pages, 1 figure

Scientific paper

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.

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