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Cyclic coverings of virtual link diagrams

Graduate School of Natural Sciences, Nagoya City University, Nagoya, Japan

E-mail Address: kamada@nsc.nagoya-cu.ac.jp

https://doi.org/10.1142/S0129167X19500721Cited by:4 (Source: Crossref)

Abstract

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

Keywords:

AMSC: 57M25, 57M27

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