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 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.