Double branched covers of knotoids

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in S2, 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 reversibility and other properties in the hyperbolic case. Moreover, with our construction we are able to detect both the trivial knotoid in S2 and the trivial knotoid in D2.

Duke Scholars

Author Dorothy Buck Mathematics