Double branched covers of knotoids
Geometric Topology
2019-09-26 v2
Abstract
By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in the 2-sphere, up to orientation reversion and rotation, and knots with a strong inversion, up to conjugacy. This correspondence allows us to study knotoids through tools and invariants coming from knot theory. In particular, concepts from geometrisation generalise to knotoids, allowing us to characterise invertibility and other properties in the hyperbolic case. Moreover, with our construction we are able to detect both the trivial knotoid in the 2-sphere and the trivial planar knotoid.
Keywords
Cite
@article{arxiv.1811.09121,
title = {Double branched covers of knotoids},
author = {Agnese Barbensi and Dorothy Buck and Heather A. Harrington and Marc Lackenby},
journal= {arXiv preprint arXiv:1811.09121},
year = {2019}
}
Comments
39 pages, 40 figures. It incorporates the referees' comments and a small change in Theorem 1.3