Geodesic
Classification of virtual string links up to cobordism
Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 37-49.

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Cobordism of virtual string links on n strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links on n strands up to cobordisms and elements of the direct product of n(n − 1) copies of the integers. This paper also shows that virtual string links up to unwelded equivalence are classified by those groups. Finally, the related theory of welded string link cobordism is defined herein and shown to be trivial for string links with one component.
DOI : 10.26493/1855-3974.2025.5d9
Keywords: Virtual links, string links, cobordism, concordance, welded knots 
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Robin Gaudreau. Classification of virtual string links up to cobordism. Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 37-49. doi : 10.26493/1855-3974.2025.5d9. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2025.5d9/

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