Journal of the
Korean Mathematical Society JKMS

In this paper, we construct infinite families of knots in $S^3$ which admit Dehn surgery producing a graph manifold which consists of two Seifert-fibered spaces over the disk with two exceptional fibers, glued together along their boundaries. In particular, we show that for any natural numbers $a,b,c,$ and $d$ with $a\geq 3$ and $b,c,d\geq 2$, there are knots in $S^3$ admitting a graph manifold Dehn surgery consisting of two Seifert-fibered spaces over the disk with two exceptional fibers of indexes $a$, $b$, and $c$, $d$, respectively.

Keywords: knots, Dehn surgery, graph manifolds, Seifert curves, twisted torus knots, R-R diagrams

MSC numbers: Primary 57M25