Abstract Let be a regular local ring and non‐zero element of . A theorem due to Knörrer states that there are finitely many isomorphism classes maximal Cohen–Macaulay (CM) ‐modules if only the same is true for double branched cover , is, hypersurface which defined by in We consider an analogue this statement case instead In particular, we show hypersurface, refer as ‐fold has finite CM represen...

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in 2-sphere, up to orientation reversion and rotation, knots with strong inversion, conjugacy. This allows us study through tools invariants coming from knot theory. In particular, concepts geometrisation generalise knotoids, allowing characterise invertibility other properties hyperbolic ca...