Virtual Crossing Number and the Arrow Polynomial

Abstract

We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus.

28 pages, 35 figures v2: Updated bibliography and Soulie knot v3: Updated bibliography and bound on genus

References in corpus (4)

• Minimal surface representations of virtual knots and links
• Pants Decompositions of Surfaces
• An Extended Bracket Polynomial for Virtual Knots and Links
• On Virtual Crossing Number Estimates For Virtual Links