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Links and Planar Diagram Codes

Matt Mastin
Organization: Wake Forest University
Department: Department of Mathematics
Journal / Anthology

Journal of Knot Theory and Its Ramifications
Year: 2015
Volume: 24
Issue: 3

In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code (PD-Code). PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan et al. We present the set of PD-codes as a standalone object and discuss its relationship with link diagrams. We give an explicit algorithm for reconstructing a knot diagram on a surface from a PD-code. We also discuss the intrinsic symmetries of PD-codes (i.e. invertibility and chirality). The moves analogous to the Reidemeister moves are also explored, and we show that the given set of PD-codes modulo these combinatorial Reidemeister moves is equivalent to classical link theory.

*Mathematics > Topology