Gauss diagrams of real and virtual knots in the solid torus

Abstract

We define a new kind of Gauss diagrams to describe knots in the solid torus with projections in the annulus. We see that it provides an efficient tool for showing that a knot diagram can be fully recovered from its decorated Gauss diagram, and we use it to establish a characterization of the decorated Gauss diagrams of closed braids.

arXiv comment19 pages, 15 figures

Cited by in corpus (1)

• On possible existence of HOMFLY polynomials for virtual knots