| Equivalent Separating Curves on Closed Surface of Genus 2 |
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| 作者姓名： | 沈广艳 雷逢春 |
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| 作者单位： | Department of Mathematics Northeastern Normal University Changchun，130021，Department of Mathematics Harbin Institute of Technology，Harbin，150001 |
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| 基金项目： | The NSF (10171024,10471020) of Chinaa grant of the outstanding Youth fellowship of Hei Long Jiang Province and the Science Foundation (20060106) for Yong Teachers of Northeast Normal University. |
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| 摘 要： | Let {A,B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to (A, B) if it is disjoint from A∪B and it cuts F into two once-punctured tori X, Y with A(?)X, B(?)Y. Letγbe a simple closed curve on F which is disjoint from A∪B and intersects C essentially in two points. In this paper, we show that up to isotopy, {hnγ(C):n∈Z} is the set containing all the simple closed curves on F which is separating with respect to (A,B), where hγis the Dehn twist alongγon F. This also shows how two simple closed curves on F which are separating with respect to (A,B) are related. The result can be applied to yield all Haken spheres of a Heegaard splitting V∪F W which are weakly equivalent to a given Heken sphere of the splitting.
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| 关 键 词： | 分裂曲线 Haken球面 不相交 等价物 |
Equivalent Separating Curves on Closed Surface of Genus 2 |
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| SHEN Guang-yan.Equivalent Separating Curves on Closed Surface of Genus 2[J].Northeastern Mathematical Journal,2006,22(2):193-198. |
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| Authors: | SHEN Guang-yan |
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| Institution: | [1]Department of Mathematics, Northeastern Normal University, Changchun, 130021 [2]Department of Mathematics, Harbin Institute of Technology, Harbin, 150001 |
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| Abstract: | |
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| Keywords: | separating curve with respect to a partition Dehn twist Haken sphere |
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