Classification of virtual string links up to cobordism

Authors

DOI:

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

Keywords:

Virtual links, string links, cobordism, concordance, welded knots

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.

Published

2020-10-29

Issue

Section

Articles