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有亏格为1的Heegaard分解的三维流形中的环面纽结

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数学年刊（A辑） 2024年第1期45卷 1-14页

作者：徐妍雷逢春李风玲梁良大连理工大学数学科学学院辽宁大连116024 辽宁师范大学数学学院辽宁大连116029

将存在亏格为1的Heegaard分解T’_(1)∪F T’_(2)的三维流形记为M=L(p,q),其中p和q是互素整数,q/p为T’_(2)的纬线在T’_(1)上的斜率.若环面F上的简单闭曲线γ在M中非平凡,则称γ是M中的环面纽结.本文对在M中沿环面纽结作m/n-Dehn手术... 详细信息

将存在亏格为1的Heegaard分解T’_(1)∪F T’_(2)的三维流形记为M=L(p,q),其中p和q是互素整数,q/p为T’_(2)的纬线在T’_(1)上的斜率.若环面F上的简单闭曲线γ在M中非平凡,则称γ是M中的环面纽结.本文对在M中沿环面纽结作m/n-Dehn手术所得流形进行了分类,并给出了两个实心环体沿边界上平环作融合所得流形是L(p,q)中环面纽结补的特征描述.

关键词： H’-分解透镜空间环面纽结 Seifert流形

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2-Compressible non-Heegaard surfaces in small 3-manifolds

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Science China Mathematics 2005年第11期48卷 1499-1504页

作者： lei fengchun GUO Xiao Department of Mathematics Harbin Institute of Technology Harbin 150001 China Department of Mathematics Harbin Institute of Technology Harbin 150001 China

In the present paper, we investigate the non-Heegaard 2-compressible surfaces in small 3-manifolds, and show that such surfaces have some good properties.

关键词： compressible surface,2-compressible surface,small 3-manifold

A standard form of incompressible surfaces in 3-dimensional handlebodies

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Science China Mathematics 2023年第10期66卷 2309-2324页

作者： Wei Lin fengchun lei School of Mathematical Sciences Dalian University of TechnologyDalian 116024China

Applying the Morse theory,we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional *** also give a necessary and sufficient condition to determine the incompressibility of such surfaces placed in our standard *** algorithm is *** examples are given to test the algorithm.

关键词： incompressible surface handlebody Morse theory general position

Topologically minimal surfaces versus self-amalgamated Heegaard surfaces

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Science China Mathematics 2014年第11期57卷 2393-2398页

作者： E Qiang lei fengchun School of Mathematical Sciences Dalian University of Technology

Let V ∪SW be a Heegaard splitting of M,such that αM = α-W = F1 ∪ F2 and g(S) = 2g(F1)= 2g(F2). Let V * ∪S*W * be the self-amalgamation of V ∪SW. We show if d(S) 3 then S* is not a topologically minimal surface.

关键词： 3-manifolds self-amalgamation Heegaard surfaces topologically minimal surfaces

Virtual Braids,Virtual Temperley-Lieb Algebra and f-Polynomial

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Chinese Annals of Mathematics,Series B 2017年第6期38卷 1275-1286页

作者： Zhiguo LI fengchun lei Jingyan LI School of Science Hebei University of TechnologyTianjin 300401China Department of Mathematics Dalian University of TechnologyDalian 116024LiaoningChina. Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang 050043China.

The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra,... 详细信息

关键词： Virtual braids Virtual Temperley-Lieb algebra f-polynomial

On 3-Submanifolds of S3 Which Admit Complete Spanning Curve Systems

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Chinese Annals of Mathematics,Series B 2017年第6期38卷 1373-1380页

作者： Yan ZHAO fengchun lei Fengling LI School of Mathematical Sciences Dalian University of TechnologyDalian 116024LiaoningChina Department of General Platform Beijing Information Technology CollegeChina

Let M be a compact connected 3-submanifold of the 3-sphere S^3 with one boundary component F such that there exists a collection of n pairwise disjoint connected orientable surfaces S = {S_1, ···, S_n} properly embedded in M, ?S = {?S_1, ···, ?S_n}is a complete curve system on F. We call S a complete surface system for M, and ?S a complete spanning curve system for M. In the present paper, the authors show that the equivalent classes of complete spanning curve systems for M are unique, that is, any complete spanning curve system for M is equivalent to ?S. As an application of the result,it is shown that the image of the natural homomorphism from the mapping class group M(M) to M(F) is a subgroup of the handlebody subgroup Hn.

关键词： Complete surface system Complete spanning curve system Heegaarddiagram Handlebody addition

Unstabilized and uncritical self-amalgamation along essential subsurfaces

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Science China Mathematics 2019年第9期62卷 1807-1812页

作者： Liang Liang Fengling Li fengchun lei School of Mathematics Liaoning Normal UniversityDalian116029China School of Mathematical Sciences Dalian University of TechnologyDalian116024China

Suppose V ∪S W is a strongly irreducible Heegaard splitting of a compact connected orientable 3-manifold M and F1 and F2 are pairwise disjoint homeomorphic essential subsurfaces in ?V. In this paper,we give a suffici... 详细信息

关键词： self-amalgamation curve complex stabilization critical surface

A necessary and sufficient condition for a surface sum of two handlebodies to be a handlebody

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Science China Mathematics 2020年第10期63卷 1997-2004页

作者： fengchun lei He Liu Fengling Li Andrei Vesnin School of Mathematical Sciences Dalian University of TechnologyDalian 116024China Regional Scientific and Educational Mathematical Center Department of Mechanics and MathematicsTomsk State UniversityTomsk 634050Russia

The main results of the paper are that we give a necessary and sufficient condition for a surface sum of two handlebodies along a connected surface to be a handlebody as follows:(1)The annulus sum H=H1∪AH2 of two handlebodies H1 and H2 is a handlebody if and only if the core curve of A is a longitude for either H1 or H2;(2)Let H=H1∪Sg,b H2 be a surface sum of two handlebodies H1 and H2 along a connected surface S=Sg,b,b 1,ni=g(Hi)2,i=1,*** that S is incompressible in both H1 and *** H is a handlebody if and only if there exists a basis J={J1,...,Jm}with a partition(J1,J2)of J such that J1 is primitive in H1 and J2 is primitive in H2.

关键词： handlebody surface sum of 3-manifolds free group

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