## The Michigan Mathematical Journal

### Extensions of Some Classical Local Moves on Knot Diagrams

#### Abstract

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.

#### Article information

Source
Michigan Math. J., Volume 67, Issue 3 (2018), 647-672.

Dates
Revised: 20 June 2017
First available in Project Euclid: 13 July 2018

https://projecteuclid.org/euclid.mmj/1531447373

Digital Object Identifier
doi:10.1307/mmj/1531447373

Mathematical Reviews number (MathSciNet)
MR3835567

Zentralblatt MATH identifier
06969987

#### Citation

Audoux, Benjamin; Bellingeri, Paolo; Meilhan, Jean-Baptiste; Wagner, Emmanuel. Extensions of Some Classical Local Moves on Knot Diagrams. Michigan Math. J. 67 (2018), no. 3, 647--672. doi:10.1307/mmj/1531447373. https://projecteuclid.org/euclid.mmj/1531447373

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