Intersection formulas for parities on virtual knots

2021/10/15 by Nikonov, Igor
#57K12 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2110.08392

Abstract

We prove that parities on virtual knots come from invariant 1-cycles on the arcs of knot diagrams. In turn, the invariant cycles are determined by quasi-indices on the crossings of the diagrams. The found connection between the parities and the (quasi)-indices allows to define a new series of parities on virtual knots.

Related

• Parity Biquandle Invariants of Virtual Knots
• The intersection polynomials of a virtual knot I: Definitions and calculations
• The intersection polynomials of a long virtual knot I: Definitions and properties
• Two-variable Parity Polynomial for Virtual Knotoids
• A Functorial Map from Virtual Knots to Classical Knots and\n Generalisations of Parity