Invariants of virtual links and twisted links using affine indices

Abstract

The affine index polynomial and the $n$-writhe are invariants of virtual knots which are introduced by Kauffman and by Satoh and Taniguchi independently. They are defined by using indices assigned to each classical crossing, which we call affine indices in this paper. We discuss a relationship between the invariants and generalize them to invariants of virtual links. The invariants for virtual links can be also computed by using cut systems. We also introduce invariants of twisted links by using affine indices.