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The problem we consider in this paper was raised in [3]. Suppose T is a torus on the boundary of an orientable 3-manifold X, and S is a surface on ∂X − T which is incompressible in X. A slope γ is the isotopy class of a nontrivial simple closed curve on T. Denote by X(γ) the manifold obtained by attaching a solid torus to X so that γ is the slope of the(More)
A compact orientable surface F with nonnegative Euler characteristic is either a sphere, a disk, a torus, or an annulus. If a 3-manifold M contains such an essential surface, then it is said to be reducible, ∂-reducible, toroidal, or annular, respectively. Any such surface can be used to decompose the manifold further into simpler manifolds. We say that M(More)
Suppose M is a hyperbolic 3-manifold which admits two Dehn fillings M(r 1) and M(r 2) such that M(r 1) contains an essential torus and M(r 2) contains an essential annulus. It is known that ∆ = ∆(r 1 , r 2) ≤ 5. We will show that if ∆ = 5 then M is the Whitehead sister link exterior, and if ∆ = 4 then M is the exterior of either the Whitehead link or the(More)
1 Steinhaus conjectured that every closed oriented C 1-curve has a pair of anti-parallel tangents. The conjecture is not true. Porter [Po] showed that there exists an un-knotted curve which has no anti-parallel tangents. Colin Adams rised the question of whether there exists a nontrivial knot in R 3 which has no parallel or antiparallel tangents. In this(More)
Abby Thompson proved that if a link K is in thin position but not in bridge position then the knot complement contains an essential meridional planar surface, and she asked whether some thin level surface must be essential. This note is to give a positive answer to this question, showing that the if a link is in thin position but not bridge position then a(More)
This paper studies Dehn surgery on a large class of links, called arborescent links. It will be shown that if an arborescent link L is suuciently complicated, in the sense that it is composed of at least 4 rational tangles T (p i =q i) with all q i > 2, and none of its length 2 tangles are of the form T (1=2q 1 ; 1=2q 2), then all complete surgeries on L(More)
The Nielsen Conjecture for Homeomorphisms asserts that any homeo-morphism f of a closed manifold is isotopic to a homeomorphism realizing the Nielsen number of f , which is a lower bound for the number of fixed points among all maps homotopic to f. The main theorem of this paper proves this conjecture for all orientation preserving homeomorphisms on(More)
We show that if a simple 3-manifold M has two Dehn fillings at distance ∆ ≥ 4, each of which contains an essential annulus, then M is one of three specific 2-component link exteriors in S 3. One of these has such a pair of annular fillings with ∆ = 5, and the other two have pairs with ∆ = 4. §1. Introduction Let M be a (compact, connected, orientable)(More)