Open Access
July, 2017 On usual, virtual and welded knotted objects up to homotopy
Benjamin AUDOUX, Paolo BELLINGERI, Jean-Baptiste MEILHAN, Emmanuel WAGNER
J. Math. Soc. Japan 69(3): 1079-1097 (July, 2017). DOI: 10.2969/jmsj/06931079


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.


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Benjamin AUDOUX. Paolo BELLINGERI. Jean-Baptiste MEILHAN. Emmanuel WAGNER. "On usual, virtual and welded knotted objects up to homotopy." J. Math. Soc. Japan 69 (3) 1079 - 1097, July, 2017.


Published: July, 2017
First available in Project Euclid: 12 July 2017

zbMATH: 06786989
MathSciNet: MR3685036
Digital Object Identifier: 10.2969/jmsj/06931079

Primary: 57M25 , 57M27
Secondary: 20F36

Keywords: braids , Gauss diagrams , link homotopy , self-virtualization , string links , virtual and welded knot theory

Rights: Copyright © 2017 Mathematical Society of Japan

Vol.69 • No. 3 • July, 2017
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