Cyclic surgery on genus one knots (Q1355881)

The real projective 3-space (or the lens space of type \((2,1)\)) is obtained by Dehn surgery on a trivial knot. There is a conjecture that no Dehn surgery on a nontrivial knot yields the real projective 3-space. It is known to be true in the cases that knots are composite knots, torus knots, alternating knots, satellite knots, and symmetric knots. In the paper under review, the author shows that the real projective 3-space cannot be obtained by Dehn surgery on a genus one knot by the argument of Scharlemann cycle.