A Gordon–Luecke-type argument for knots in lens spaces

Certain knots in projective 3-space are shown not to allow nontrivial Dehn surgery that yields projective 3-space again. To do this, the techniques used by Gordon–Luecke for knots in S3 are generalized to lens spaces. Graphs are constructed in nonorientable surfaces instead of 2-spheres, and the sign for vertices is replaced by a sign for edges.