Ying-Qing Wu
We use sutured manifold theory, essential laminations and essential branched surfaces to establish the upper bounds of distances between certain types of nonsimple Dehn surgery slopes. This is the revised version of an earlier preprint {\it Dehn surgery and simple manifolds.}
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We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0-- or 1--crossing knot. The proof uses techniques from sutured manifold theory.
Stretch laminations and hyperbolic Dehn surgery
研究双曲3流形Dehn手术族中最佳Lipschitz圆值映射的最大拉伸叶状结构，基于Thurston范数和Dehn填充斜率长度给出准则判断其何时为填充核心曲线并集，并证明存在无穷多例子使叶状结构仅含闭叶，为无限循环覆盖中的轨道闭包提供信息。
A persistent lamination for a knot K is an essential lamination in the complement of K, which remains essential after every non-trivial Dehn surgery along K. Having a persistent lamination implies, for example, that every manifold obtained by non-trivial Dehn surgery along K has universal cover R^3. In this paper we present a method for building persistent laminations for knots from an incompressible Seifert surface for some `parent' knot. Using this construction, we can, for example, currently build persistent laminations for approximately 45 percent of the knots in the standard knot tables; …
We study Dehn surgeries on null-homotopic knots that yield fibred $3$--manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai's theory of sutured manifold decomposition. Such surgeries are negative examples to a question of Michel Boileau. Another result we will prove is about surgeries which reduce the Thurston norm of a fibred manifold.
A persistent lamination for a knot K is an essential lamination in the complement of the K, which remains essential after every non-trivial Dehn surgery along K. In particular, this implies that all of the Dehn surgery manifolds have universal cover R^3. This paper presents a method for building tangles T with the property that every knot K obtained by tangle sum with T has a persistent lamination. A natural generalization to 2n-string tangles is also given.
Attaching a 2-handle to a genus two or greater boundary component of a 3-manifold is a natural generalization of Dehn filling a torus boundary component. We prove that there is an interesting relationship between an essential surface in a sutured 3-manifold, the number of intersections between the boundary of the surface and one of the sutures, and the cocore of the 2-handle in the manifold after attaching a 2-handle along the suture. We use this result to show that tunnels for tunnel number one knots or links in any 3-manifold can be isotoped to lie on a branched surface corresponding to a ce…
We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot $β$ in a compact, orientable, hyperbolic 3-manifold $M$ has the property that winding number and wrapping number are not equal with respect to a non-trivial class in $H_2(M,\boundary M)$, then, with only a few possible exceptions, every 3-manifold $M'$ obtained by Dehn surgery on $β$ with surgery distance $Δ\geq 2$ will be hyperbolic.
We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured laminations in S, equipped with its natural Lebesgue measure. We prove that, for any 3-manifold M, the set of curves c on a Heegaard surface S in M, such that every non-trivial Dehn twist at c yields a Heegaard splitting of high distance, is generic in the set of all essential simple closed curves on S. Our definition of "genericity" is different and more intrinsic th…
Sutured manifold hierarchies and the Thurston norm
本文通过maw双图构造，提出从缝合流形层次结构中提取图登森规范信息的方法，并应用此方法计算了某些结的图登森规范，反驳了Baker-Taylor的问题。
Endperiodic maps, splitting sequences, and branched surfaces
本文通过证明端期映射具有周期性分裂序列，加强了Gabai和Mosher的定理，展示了veering分支表面在缝合 manifold 中的应用及理论扩展。
The purpose of this paper is to classify Anosov flows on the 3-manifolds obtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is denoted by M(r) (r is a ratioanl number), which contains the first class of hyperbolic 3-manifolds admitting Anosov flows in history, discovered by Goodman. Combining with the classification of Anosov flows on the sol-manifold M(0) due to Plante, we have: 1. if r is an integer, up to topological equivalence, M(r) exactly carries a unique Anosov flow, which is constructed by Goodman by doing a Dehn-Fried-Goodman surgery on a suspension Anosov f…
Bending parameterization of geometrically finite hyperbolic manifolds
本文证明非 Fuchs 型几何有限双曲结构由弯曲叶状结构唯一确定，弯曲映射为同胚，推广了凸余紧情形，并建立了边界纤维可收缩性判据。
A knot K is called n-adjacent to another knot K', if K admits a projection containing n generalized crossings such that changing any 0 < m \leq n of them yields a projection of K'. We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to answer the question of the extent to which non-isotopic knots can be adjacent to each other. A consequence of our main result is that if K is n-adjacent to K' for all n, then K and K' are isotopic. This provides a partial verification of the conjecture of V. Vassiliev that the finite type…
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