English

Double coverings of twisted links

Geometric Topology 2016-01-12 v3

Abstract

Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the notion of the double covering of a twisted link. It is defined by considering the orientation double covering of an abstract link or alternatively by constructing a diagram called a double covering diagram. We also discuss links in thickened surfaces, their diagrams and their stable equivalence classes. Bourgoin's twisted knot group is understood as the virtual knot group of the double covering.

Keywords

Cite

@article{arxiv.1510.03001,
  title  = {Double coverings of twisted links},
  author = {Naoko Kamada and Seiichi Kamada},
  journal= {arXiv preprint arXiv:1510.03001},
  year   = {2016}
}