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.
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Michigan Mathematical Journal, University of Michigan, 2018, 67 (3), pp.647-672. 〈10.1307/mmj/1531447373〉
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Dernière modification le : mercredi 19 décembre 2018 - 09:27:48
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Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan, Emmanuel Wagner. Extensions of some classical local moves on knot diagrams. Michigan Mathematical Journal, University of Michigan, 2018, 67 (3), pp.647-672. 〈10.1307/mmj/1531447373〉. 〈hal-01217085〉

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