Invariants of Links in Thickened Surfaces

Abstract

A group invariant for links in thickened closed orientable surfaces is studied. Associated polynomial invariants are defined. The group detects nontriviality of a virtual link and determines its virtual genus.

knot, link, operator group, virtual link, virtual genus

References in corpus (3)

• What is a virtual link?
• Minimal surface representations of virtual knots and links
• Doubly periodic textile patterns

Cited by in corpus (8)

• Evolution method and HOMFLY polynomials for virtual knots
• A characterization of alternating links in thickened surfaces
• Representations of virtual braids by automorphisms and virtual knot groups
• Topological Surgery and its Dynamics
• Virtually Symmetric representations and marked Gauss diagrams
• On the lower central series of some virtual knot groups
• Groups of virtual trefoil and Kishino knots
• Chord index for knots in thickened surfaces