Gauss diagrams of real and virtual knots in the solid torus

2012/01/27 by Arnaud Mortier, Mortier, Arnaud
Mathematics · #57M99 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M99

paper · pdf · doi:10.48550/arxiv.1201.5859

19 pages, 15 figures

arxiv created 2012/01/27 · openalex publication_date 2012/01/27 · arxiv updated 2012/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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