Sangyop Lee

Reducing dehn fillings and small surfaces

In this paper we investigate the distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing essential small surfaces including non-orientable surfaces. In particular, we study the situations where one filling creates an essential sphere or projective plane, and the other creates an essential sphere, projective plane, annulus, M?bius band, torus or Klein bottle, for all eleven pairs of such non-hyperbolic manifolds.

TWISTED TORUS KNOTS T(p, q;kq, s) ARE CABLE KNOTS

We determine the knot types of twisted torus knots T(p, q;r, s) when q divides r. We also determine their tunnel numbers.

P 2 -reducing and toroidal Dehn fillings

Let M be a compact, connected, orientable 3-manifold with a torus boundary component

BOUNDARY STRUCTURE OF HYPERBOLIC 3-MANIFOLDS ADMITTING ANNULAR AND TOROIDAL FILLINGS AT LARGE DISTANCE

\partial_{0}M

Boundary structure of hyperbolic 3-manifolds admitting annular fillings at large distance

. A slope on

TWISTED TORUS KNOTS WITH ESSENTIAL TORI IN THEIR COMPLEMENTS

\partial_{0}M

TOROIDAL DEHN SURGERIES ON KNOTS IN S1× S2

is the isotopy class of an unoriented essential simple loop. For a slope r , the manifold obtained from M by r-Dehn filling is M ( r ) = M

TOROIDAL SURGERIES ON GENUS TWO KNOTS

\cup

Constructing persistently laminar knots

V r , where V r is a solid torus glued to M along

Knot types of twisted torus knots

\partial_{0}M