The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 67, Issue 3 (2018), 647-672.
Extensions of Some Classical Local Moves on Knot Diagrams
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.
Michigan Math. J., Volume 67, Issue 3 (2018), 647-672.
Received: 16 December 2016
Revised: 20 June 2017
First available in Project Euclid: 13 July 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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