Double coverings of twisted links

Naoko Kamada; Seiichi Kamada

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arXiv · 1510.03001

Double coverings of twisted links

Naoko Kamada·Seiichi Kamada

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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.

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BibTeX RIS

Naoko Kamada, Seiichi Kamada. 2016-01-11. Double coverings of twisted links. https://arxiv.org/abs/1510.03001

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