Journal of the Mathematical Society of Japan

On usual, virtual and welded knotted objects up to homotopy

Benjamin AUDOUX, Paolo BELLINGERI, Jean-Baptiste MEILHAN, and Emmanuel WAGNER

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 69, Number 3 (2017), 1079-1097.

Dates
First available in Project Euclid: 12 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1499846518

Digital Object Identifier
doi:10.2969/jmsj/06931079

Mathematical Reviews number (MathSciNet)
MR3685036

Zentralblatt MATH identifier
06786989

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds
Secondary: 20F36: Braid groups; Artin groups

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

Citation

AUDOUX, Benjamin; BELLINGERI, Paolo; MEILHAN, Jean-Baptiste; WAGNER, Emmanuel. On usual, virtual and welded knotted objects up to homotopy. J. Math. Soc. Japan 69 (2017), no. 3, 1079--1097. doi:10.2969/jmsj/06931079. https://projecteuclid.org/euclid.jmsj/1499846518


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