A Representation Theorem for Knots and a Generalization of the Fundamental Theorem of Finite Type Invariants

2018/06/28 by Cole Hugelmeyer, Hugelmeyer, Cole · 1 citation
Mathematics · Computer Science · #Geometric and Algebraic Topology #Logic, programming, and type systems #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1806.11201

Abstract

We provide a way to produce knots in S³ from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental theorem of finite type invariants. We also provide moves for the diagrams so that any two diagrams for the same knot are connected by a sequence of moves.

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• Encoding knots by clasp diagrams

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• Braided chord diagrams
• Finite Type Invariants of Classical and Virtual Knots
• Encoding knots by clasp diagrams
• Computing Finite Type Invariants Efficiently
• Knot Diagrammatics