Conversion to almost classical virtual links and pseudo Goeritz matrices

Abstract

The notion of a virtual link is a generalization of a classical link. Alexander numbering is a numbering of [Formula: see text] to arcs of a classical link diagram which is due to a numbering to disks of a complement of a link diagram in [Formula: see text]. Every classical link diagram admits Alexander numbering. A virtual link diagram corresponds to a link diagram in a closed oriented surface. Some virtual link diagrams do not admit any Alexander numbering. If a virtual link diagram admits Alexander numbering, we call it an almost classical virtual link diagram. In this paper, we construct a map from the set of virtual link diagrams to that of almost classical virtual link diagrams. It induces a map from the set of virtual links to that of almost classical virtual links. Using this map, we define a kind of Goeritz matrix of virtual link diagrams and introduce invariants of virtual links.