Arc-presentations of links. Monotonic simplification

By I. Dynnikov. 2002

129 citations recorded by the source corpus.

We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bd71e627bdff388f9508fd82fb4a01cd805888c3

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

A polynomial upper bound on Reidemeister moves (2013, methodology): “This is admirably described in the proof of Lemma 6 in [8], and so we only give a sketch here.”
Transverse knots distinguished by knot Floer homology (2007, background): “According to Cromwell [7] (see also [9]), two grid diagrams G1 and G2 on the torus represent isotopic knots in S 3 if and only if they can be connected by a finite sequence of the following grid moves: Commutation: For any pair of consecutive columns ofG so that theX and O from one column do not sep”
Grid Homology for Knots and Links (2015, result): “Our proof is similar in spirit to Dynnikov’s proof [37].”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “Grid diagrams are equivalent to arc presentations of links, which go back to the work of Brunn [Bru98]; see also [Cro95, Dyn06].”
A combinatorial description of knot Floer homology (2006, background): “[17]; they have enjoyed a considerable amount of attention over the years, see also [3], [4].”