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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)

- Ying-Qing Wu
- 1992

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)

- Ying-Qing Wu
- 1997

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)

- Ying-Qing Wu, Y-Q. WU
- 1999

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)

- Ying-Qing Wu, Ying-Qing Wu
- 1997

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)

A 2-handle addition on the boundary of a hyperbolic 3-manifold M is called degenerating if the resulting manifold is not hyperbolic. There are examples that some manifolds admit infinitely many degenerating handle additions. But most of them are not “basic”. (See section 1 for definitions.) Our first main theorem shows that there are only finitely many… (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)

We will determine whether a given surgery on a 2-bridge knot is reducible, toroidal, Seifert bered, or hyperbolic. In [Th1] Thurston showed that if K is a hyperbolic knot, then all but nitely many surgeries on K are hyperbolic. In particular, for the Figure 8 knot, it was shown that exactly 9 nontrivial surgeries are non-hyperbolic. Let Kp=q be a 2-bridge… (More)

- Mario Eudave-Muñoz, Ying-Qing Wu, Y-Q. WU
- 1999

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)

- Er-Wei Bai, Ying-Qing Wu
- Automatica
- 2002

In this paper, we consider the sampling of a continuous time system with possibly a non-rational transfer function. Limiting zero distribution of the sampled system represented by an FIR model is derived. It is shown that the zeros of the FIR sampled system converge evenly to the unit circle or to the unit disk plus unstable roots of the reciprocal… (More)