Cyclic coverings of virtual link diagrams

Abstract

A virtual link diagram is called mod m almost classical if it admits an Alexander numbering valued in integers modulo m, and a virtual link is called mod m almost classical if it has a mod m almost classical diagram as a representative. In this paper, we introduce a method of constructing a mod m almost classical virtual link diagram from a given virtual link diagram, which we call an m-fold cyclic covering diagram. The main result is that m-fold cyclic covering diagrams obtained from two equivalent virtual link diagrams are equivalent. Thus we have a well-defined map from the set of virtual links to the set of mod m almost classical virtual links. Some applications are also given.

Diagrams realizing prescribed sublink diagrams for virtual links and welded links

“…In order to prove Theorem 3, we use the notion of the double covering of a virtual link, introduced in [5,6].…”

“…, k} as in Figure 14. We call the diagram D a double covering diagram of D. Refer to [5,6] for details. By this theorem, the double covering is defined for a virtual link.…”