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Nielsen Theory on 3-manifolds Covered by S^2× R

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Acta Mathematica Sinica,English Series 2015年第4期31卷 615-636页

作者： Daciberg GONALVES Peter WONG Xue Zhi ZHAO Dept. de Matemtica-IME-USP Caixa Postal 66.281-CEP 05314-970So Paulo-SP Brasil Department of Mathematics Bates College Department of Mathematics & Institute of Mathematics and Interdisciplinary Science Capital Normal University

Let f ： M→ M be a self-map of a closed manifold M of dimension dim M ≥ 3. The Nielsen number N（f） of f is equal to the minimal number of fixed points of f＇ among all self-maps f＇ in the homotopy class of f. In this paper, we determine N（f） for all self-maps f when M is a closed 3-manifold with S^2× R geometry. The calculation of N（f） relies on the induced homomorphisms of f on the fundamental group and on the second homotopy group of M.

关键词： Lefschetz number Nielsen number 3-manifolds

An Algorithm of Witten's Invariants of Some 3-manifolds

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Chinese Quarterly Journal of Mathematics 1996年第2期11卷 95-97页

作者：李起升河南大学数学系河南开封 475001

In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.

关键词： witten' s invariants 3-manifolds links

Generalized Hopfian Property, a Minimal Haken Manifold, and Epimorphisms Between 3-Manifold Groups

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Acta Mathematica Sinica,English Series 2002年第1期18卷 157-172页

作者： REID Alan W Department of Mathematics. University of Texas Austin. TX 78712. USA

We address the question that if π_1-surjective maps between closed aspherical 3-manifolds have the same rank on π_1 they must be of non-zero degree. The positive answer is proved for Seifert manifolds, which is used in constructing the first known example of minimal Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3- manifolds. Many examples are given.

关键词： Non-zero degree maps Epimorphisms 3-manifolds

3-Manifold Containing Separating Incompressible Surfaces of All Positive Genera

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1315-1318页

作者： Ji Ming MA Rui Feng QIU Department of Mathematics Jilin University Changchun 130023 P. R. China Department of Mathematics Dalian University of Technology Dalian 116024 P. R. China

In this paper, we shall prove that for any orientable 3-manifold M, there is a link L - K U K1 U K2 U K3 with four components in M, such that the complement of L, say ML, contains separating essential closed surfaces ... 详细信息

关键词： Incompressible surface Knot 3-manifolds

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

On Heegaard Splittings with Finitely Many Pairs of Disjoint Compression Disks

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Journal of Mathematical Research with Applications 2023年第4期43卷 496-504页

作者： Qiang E Zhiyan ZHANG School of Science Dalian Maritime University

Suppose V ∪S W is a genus-g weakly reducible Heegaard splitting of a closed 3-manifold with finitely many pairs of disjoint compression disks on distinct sides up to isotopy and g > 2. We show V ∪S W admits an untelescoping:(V1∪S1W1) ∪F(W2∪S2V2) such that Wi has a unique separating compressing disk and d(Si) ≥ 2, for i = 1, 2. If there exist more than one but finitely many pairs of disjoint compression disks, at least one of d(Si) is 2 and S is a critical Heegaard surface.

关键词： 3-manifolds Heegaard splitting weakly reducible critical surfaces