%0 Journal Article %T On usual, virtual and welded knotted objects up to homotopy %+ Institut de Mathématiques de Marseille (I2M) %+ Laboratoire de Mathématiques Nicolas Oresme (LMNO) %+ Institut Fourier (IF ) %+ Institut de Mathématiques de Bourgogne [Dijon] (IMB) %A Audoux, Benjamin %A Bellingeri, Paolo %A Meilhan, Jean-Baptiste %A Wagner, Emmanuel %< avec comité de lecture %Z I2M %Z GT %@ 0025-5645 %J Journal of the Mathematical Society of Japan %I Maruzen Company Ltd %V 69 %N 3 %P 1079--1097 %8 2017-07 %D 2017 %Z 1507.00202 %R 10.2969/jmsj/06931079 %K Braids %K Link homotopy %K Self-virtualization %K String links %K Gauss diagrams %K Virtual and welded knot theory %Z MSC: Primary: 57M25, 57M27 Secondary: 20F36 %Z Mathematics [math]/Geometric Topology [math.GT]Journal articles %X We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between these various notions. The proofs are mainly based on the techniques of Gauss diagram formulae. %G English %2 https://hal.science/hal-01176073/document %2 https://hal.science/hal-01176073/file/1507.00202.pdf %L hal-01176073 %U https://hal.science/hal-01176073 %~ UNIV-BOURGOGNE %~ UGA %~ CNRS %~ UNIV-AMU %~ FOURIER %~ EC-MARSEILLE %~ IMB_UMR5584 %~ I2M %~ I2M-2014- %~ COMUE-NORMANDIE %~ UNICAEN %~ LMNO %~ UGA-COMUE %~ ANR