Classification of virtual string links up to cobordism

Robin Gaudreau

Abstract


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.


Keywords


Virtual links, string links, cobordism, concordance

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DOI: https://doi.org/10.26493/1855-3974.2025.5d9

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications