2019/03/08 by Naoko Kamada, Kamada, Naoko
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1903.03306
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.