Classification of virtual string links up to cobordism
Keywords:Virtual links, string links, cobordism, concordance, welded knots
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.
Articles in this journal are published under Creative Commons Attribution 4.0 International License