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Distance of Edges in the curve complex of a Surface

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Journal of Mathematical Research and Exposition 2011年第6期31卷 1092-1096页

作者： Xiu Ying SHI Feng Chun LEI The College of Continuing Education Chifeng UniversityInner Mongolia 024000P.R.China School of Mathematical Sciences Dalian University of TechnologyLiaoning 116024P.R.China

Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of *** the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path betwe... 详细信息

关键词： curve complex distance of vertices 2-path between edges 2-diameter of C(S).

Sufficient Conditions for Amalgamated 3-Manifolds to be ∂-Irreducible

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 161-172页

作者： Bing FANG Fengchun LEI Liang LIANG School of Mathematical Sciences Dalian University of TechnologyDalian 116024LiaoningChina School of Mathematics Liaoning Normal UniversityDalian 116029LiaoningChina

In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets ... 详细信息

关键词： ∂-Irreducibility Irreducibility Amalgamated 3-manifold curve complex Arc complex

Local rigidity of the Teichmüller space with the Thurston metric

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Science China Mathematics 2023年第8期66卷 1751-1766页

作者： Huiping Pan School of Mathematics South China University of TechnologyGuangzhou 510641China

We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic *** is an analogue o... 详细信息

关键词： Teichmüller space Thurston metric Royden's theorem curve complex rigidity

Non degenerating Dehn fillings on genus two Heegaard splittings of knots' complements

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Science China Mathematics 2018年第6期61卷 1099-1108页

作者： Jiming Ma Ruifeng Qiu Yanqing Zou School of Mathematical Sciences Fudan University Department of Mathematics Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University Department of Mathematics Dalian Minzu University

It is Thurston's result that for a hyperbolic knot K in S^3, almost all Dehn fillings on its complement result in hyperbolic 3-manifolds except some exceptional cases. So almost all produced 3-manifolds have the same geometry. It is known that its complement in S^3, denoted by E(K), admits a Heegaard splitting. Then it is expected that there is a similar result on Heegaard distance for Dehn fillings. In this paper, Dehn fillings on genus two Heegaard splittings are studied. More precisely, we prove that if the distance of a given genus two Heegaard splitting of E(K) is at least 3, then for any two degenerating slopes on ?E(K), there is a universal bound of their distance in the curve complex of ?E(K).

关键词： Heegaard distance Dehn filling hyperbolic knot curve complex

On reducible Heegaard splittings

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Science China Mathematics 2013年第2期56卷 221-226页

作者： SUN DongQi LEI FengChun LI FengLing School of Mathematical Sciences Dalian University of Technology College of Science Harbin Engineering University

Let Ⅴ∪S W be a reducible Heegaard splitting of genus g = g（S） ≥ 2. For a maximal prime connected sum decomposition of Ⅴ∪S W, let q denote the number of the genus 1 Heegaard splittings of S2 × S1 in the decomposition, and p the number of all other prime factors in the decomposition. The main result of the present paper is to describe the relation of p, q and dim（Cy ∩ Cw）.

关键词： curve complex Heegaard splitting reducible weakly reducible

Spanning Pre-disks in a Compression Body

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Communications in Mathematical Research 2018年第2期34卷 177-183页

作者： Liang Liang Han You-fa Li Feng-ling Zhao Lu-ying School of Mathematics Liaoning Normal University School of Mathematical Sciences Dalian University of Technology

A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.

关键词： spanning pre-disk curve complex compression body maximal collection

Weakly Disk-busting curves in the Boundary of a Compression Body

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Communications in Mathematical Research 2018年第2期34卷 171-176页

作者： Sun Meng Liang Liang School of Mathematical Sciences Heilongjiang University School of Mathematics Liaoning Normal University

Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.

关键词： handle addition curve complex subsurface projection weakly diskbusting

Subsurface 1-distance of the Handlebody

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Communications in Mathematical Research 2016年第4期32卷 375-382页

作者： SUN DONG-QI lei feng-chun College of Science Harbin Engineering UniversityHarbin150001 不详

For a handlebody H w ith dH = 5, let F belong S be an essential connected subsurface of S. Let C（S） be the curve complex of S, AC（F） be the arc and curve complex of F , D（H） belong C（S） be ... 详细信息

For a handlebody H w ith dH = 5, let F belong S be an essential connected subsurface of S. Let C（S） be the curve complex of S, AC（F） be the arc and curve complex of F , D（H） belong C（S） be the disk complex of H and πf（D （H ）） belong AC（F） be the image of D （H） in AC （F）. We introduce the definition of subsurface 1-distance between the 1-simplices of AC（F） and show that under some hypothesis, πF（D（H）） comes within subsurface 1-distance at most 4 of every 1-simplex of AC （F）.

关键词： handlebody curve complex arc and curve complex subsurface 1-distance