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Article Dans Une Revue Michigan Mathematical Journal Année : 2018

Extensions of some classical local moves on knot diagrams

Jean-Baptiste Meilhan

Résumé

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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Dates et versions

hal-01217085 , version 1 (19-10-2015)

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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, 2018, 67 (3), pp.647-672. ⟨10.1307/mmj/1531447373⟩. ⟨hal-01217085⟩
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