%0 Journal Article
%T On forbidden moves and the Delta move
%A Benjamin Audoux
%A Paolo Bellingeri
%A Jean-Baptiste Meilhan
%A Emmanuel Wagner
%J Mathematics
%D 2015
%I arXiv
%X We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, $\Delta$ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to $\Delta$ moves, the notions of links and string links coincide, and that they are classified by the (virtual) linking numbers; we also prove that the $\Delta$ move is an unknotting operation for welded (long) knots. For welded knotted objects, we prove that forbidden moves imply the $\Delta$ 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.
%U http://arxiv.org/abs/1510.04237v1