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Two-dimensional submanifolds in non-simply connected 4-manifolds

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Chinese Science Bulletin 1995年第23期40卷 1949-1953页

作者：高红铸 Department of Mathematics Beijing Normal University Beijing 100875 China

A foundamental problem in 4-dimensional differential topology iS to find a surface with minimal genus that can represent a given two-dimensional homology class. Hsiang, Rohlin have got some results about the homological l-connected manifolds. This note will discuss this problem under the condition that H1（N4） is finite. Under this assumption, the possible normal Euler numbers of embedding nonorientable surfaces in 4-manifolds are also determined.

关键词： 4-manifold submanifold normal Euler number.

ON NORMAL EULER NUMBERS OF EMBEDDING RP^2 IN INDEFINITE 4-manifoldS

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Chinese Science Bulletin 1991年第23期36卷 1940-1942页

作者：高红铸 Institute of Systems Science Academia Sinica Beijing 100080 PRC

Let N be a closed, nonorientable surface, M be a simply connected 4-manifold. f: N→M is an embedding with normal bundle vf. The normal Euler class e（vf） of f is an element in H2（N,）, where is the local coefficient determined by w1（vf） =w1（N）. It is very important to determine e（vf）[N] for all embeddings. This problem is closely related to whether a two-dimensional homology class can be represented by a smooth embedded sphere. In this note, we determine all the possible normal Euler numbers of embedding real projective plane into indefinite 4-manifolds.

关键词： 4-manifold normal Euler number embedding

Cyclic Group Action of Composite Order on Indefinite 4-manifolds

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Communications in Mathematical Research 2011年第3期27卷 200-206页

作者： LI HONG-XIA LIU XI-MIN Department of Applied Mathematics Shanghai Maritime University Shanghai 201306 Department of Mathematics South China University of Technology Guangzhou 510641

In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especi... 详细信息

关键词： periodic map 4-manifold indefinite permutation representation

NORMAL EULER NUMBERS OF EMBEDDING NONORIENTABLE SURFACES IN 4-manifoldS

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Systems Science and Mathematical Sciences 1996年第3期9卷 242-251页

作者： GAO Hongzhu (Department of Mathematics, Beijing Normal University, Beijing,China) 北京师范大学数学系北京

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关键词： Normal Euler number embed 4-manifold

Branched Coverings and Embedded Surfaces in Four-manifolds

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Communications in Mathematical Research 2013年第4期29卷 370-376页

作者： Liu Xi-min Wu Yu-lai Lei Feng-chun School of Mathematical Sciences Dalian University of Technology

In this paper, we get a lower bound on the genera of surfaces re, presenting certain divisible classes in some 4-manifold X with Hi（X; Z） finite.

关键词： embedded surface 4-manifold genus

Rational-slice Knots via Strongly Negative-amphicheiral Knots

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Communications in Mathematical Research 2009年第2期25卷 177-192页

作者： Kawauchi Akio Department of Mathematics Osaka City University

We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the O-surgery manifold of a certain strongly negative amphicheiral knot such as the figure-eight knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 2-sphere if and only if the modulo two reduction of it is zero.

关键词： rational-slice knot strongly negative-amphicheiral knot O-surgery rational cobordism 4-manifold