Extensions of some classical local moves on knot diagrams

Abstract : We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of links and string links coincide, and that they are classified by the (virtual) linking numbers; we also prove that the ∆ move is an unknotting operation for welded (long) knots. For welded knotted objects, we prove that forbidden moves imply the ∆ move, the self-crossing change and the self-virtualization, and that these four local moves yield pairwise different quotients, while they collapse to only two distinct quotients in the classical case.
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Michigan Mathematical Journal, University of Michigan, 2017
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  • HAL Id : hal-01217085, version 1

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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, 2017. 〈hal-01217085〉

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