Open Access
August 2018 Extensions of Some Classical Local Moves on Knot Diagrams
Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan, Emmanuel Wagner
Michigan Math. J. 67(3): 647-672 (August 2018). DOI: 10.1307/mmj/1531447373


We consider local moves on classical and welded diagrams: (self-)crossing change, (self-)virtualization, virtual conjugation, Delta, fused, band-pass, and welded band-pass moves. Interrelationships between these moves are discussed, and, for each of these moves, we provide an algebraic classification. We address the question of relevant welded extensions for classical moves in the sense that the classical quotient of classical object embeds into the welded quotient of welded objects. As a byproduct, we obtain that all of the local moves mentioned are unknotting operations for welded (long) knots. We also mention some topological interpretations for these combinatorial quotients.


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Benjamin Audoux. Paolo Bellingeri. Jean-Baptiste Meilhan. Emmanuel Wagner. "Extensions of Some Classical Local Moves on Knot Diagrams." Michigan Math. J. 67 (3) 647 - 672, August 2018.


Received: 16 December 2016; Revised: 20 June 2017; Published: August 2018
First available in Project Euclid: 13 July 2018

zbMATH: 06969987
MathSciNet: MR3835567
Digital Object Identifier: 10.1307/mmj/1531447373

Primary: 20F36 , 57M25 , 57M27

Rights: Copyright © 2018 The University of Michigan

Vol.67 • No. 3 • August 2018
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