Non-integral toroidal surgery on hyperbolic knots in $S^3$
We show that on any hyperbolic knot in $S^3$ there is at most one non-integral Dehn surgery which yields a manifold containing an incompressible torus.
math.GT↗
arXiv subjects
Cameron McA. Gordon
Publications and source records attributed to Cameron McA. Gordon.
Combinatorial methods in Dehn surgery
This is an expository paper, in which we give a summary of some of the joint work of John Luecke and the author on Dehn surgery. We consider the situation where we have two Dehn fillings $M(α)$ and $M(β)$ on a given 3-manifold $M$, each containing a surface that is either essential or a Heegaard surface. We show how a combinatorial analysis of the graphs of intersection of the two corresponding punctured surfaces in $M$ enables one to find faces of these graphs which give useful topological information about $M(α)$ and $M(β)$, and hence, in certain cases, good upper bounds on the intersection number $Δ(α, β)$ of the two filling slopes.
math.GT↗