1 research outputs found
Knots with distinct primitive/primitive and primitive/Seifert representatives
Berge introduced knots that are primitive/primitive with respect to the genus
2 Heegaard surface, , in ; surgery on such knots at the surface slope
yields a lens space. Later Dean described a similar class of knots that are
primitive/Seifert with respect to ; surgery on these knots at the surface
slope yields a Seifert fibered space. Here we construct a two-parameter family
of knots that have distinct primitive/Seifert embeddings in with the same
surface slope, as well as a family of torus knots that have a
primitive/primitive representative and a primitive/Seifert representative with
the same surface slope.Comment: 12 pages, 8 figures; 2 figures update