Ying-Qing Wu

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Suppose M is a 3-manifold with torus T as a boundary component, and let P be an incompressible surface on ∂M disjoint from T . It was proved in [9] that in most cases, P remains incompressible in most of the Dehn filled manifolds M(γ). (See Proposition 2 below). The present note is to solve a problem posed informally by Peter Shalen, which asks whether a(More)
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)
This article is solicited by C. Adams for a special issue of Chaos, Solitons and Fractals devoted to knot theory and its applications. We present some recent results about Dehn surgeries on arborescent knots and links. In this survey we will present some recent results about Dehn surgeries on arborescent knots and links. Arborescent links are also known as(More)
Suppose M is a hyperbolic 3-manifold which admits two Dehn fillings M(r1) and M(r2) such that M(r1) contains an essential torus and M(r2) contains an essential annulus. It is known that ∆ = ∆(r1, r2) ≤ 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 2-bridge(More)
Knots are idealized 1-dimensional loops that tangle themselves in 3-space. They have been studied, for more than 100 years, primarily as abstract mathematical objects even though the original interest in the subject seems to be based in physics. There is now interest in reinvesting the mathematical abstractions with physical-like properties such as(More)
In this paper we will give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and ∂-reducible. A manifold in the second family has boundary consisting of two tori, and admits(More)