Double branched covers of knotoids

摘要

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in S-2, 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 particu-lar, concepts from geometrisation generalise to knotoids, allowing us to characterise reversibility and other properties in the hyper-bolic case. Moreover, with our construction we are able to detect both the trivial knotoid in S-2 and the trivial knotoid in D-2.