Destabilizing Heegaard splittings of knot exteriors

Tsuyoshi Kobayashi; Toshio Saito

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Destabilizing Heegaard splittings of knot exteriors

机译：结外部的Heegaard劈裂使系统不稳定

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摘要

We give a necessary and sufficient condition for Heegaard splittings of knot exteriors to admit destabilizations. As an application, we show the following: let K_1 and K_2 be a pair of knots which is introduced by Morimoto as an example giving degeneration of tunnel number under connected sum. The Heegaard splitting of the exterior of K_1 # K_2 derived from certain minimal unknotting tunnel systems of K_1 and K_2 is stabilized.

机译：我们为Heegaard结外部的分裂提供了充要条件，以使其具有稳定性。作为一个应用程序，我们显示以下内容：令K_1和K_2为一对结点，这是由Morimoto引入的示例，给出了在连接总和下退化隧道数的示例。由K_1和K_2的某些最小不通孔隧道系统得出的K_1＃K_2外部的Heegaard分裂得以稳定。

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来源
《Topology and its applications》 |2010年第1期|202-212|共11页
作者
Tsuyoshi Kobayashi; Toshio Saito;
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作者单位

Graduate School of Humanities and Sciences, Nara Women's University, Kitauoya Nishimachi, Nara 630-8506, Japan;

Department of Mathematics, South Hall, Room 6607, University of California, Santa Barbara, CA 93106, USA;

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正文语种 eng
中图分类
关键词
heegaard splitting; unknotting tunnel system; destabilization;

机译：暴风雪分裂不通的隧道系统;不稳定;

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1. On Heegaard splittings of knot exteriors with tunnel number degenerations [J] . Morimoto Kanji Topology and its applications . 2015,第DECaPTaB期

机译：关于隧道数退化的结外表面的Heegaard分裂
2. On critical heegaard splittings of tunnel number two composite knot exteriors [J] . Kim J. Journal of knot theory and its ramifications . 2013,第11期

机译：在二号复合复合隧道外部临界暴风雨劈裂中
3. Common stabilizations of Heegaard splittings of knot exteriors [J] . Jung Hoon Lee Journal of the Korean Mathematical Society . 2010,第1期

机译：结外部的Heegaard劈裂的常见稳定作用
4. Theoretical analysis of resonant mode splitting in a single microfiber knot-ring resonator [C] . Yu Jianhui, Jin Shaoshen, Lu Huihui, International Conference on Numerical Simulation of Optoelectronic Devices . 2013

机译：超细纤维结环谐振器中谐振模分裂的理论分析
5. High distance knots in closed 3-manifolds and alpha-sloped generalized Heegaard splittings of 3-manifolds. [D] . Moore, Marion. 2010

机译：闭合的3个流形和3个流形的alpha倾斜广义Heegaard分裂的高距离结。
6. Splitting linking knotting and solitonic escape of topological defects in nematic drops with handles [O] . Mykola Tasinkevych, Michael G. Campbell, Ivan I. Smalyukh 2014

机译：带柄向列液滴中的拓扑缺陷的分裂链接打结和孤子逃逸
7. Destabilizing Heegaard splittings of knot exteriors [O] . Kobayashi Tsuyoshi, Saito Toshio 2010

机译：结外表面的Heegaard劈裂导致不稳定
8. On the Choice of the Exterior Knots in the B-Spline Basis for a Spline Space [R] . Kozak, J. 1980

机译：关于样条空间B样条基外部结的选择

Destabilizing Heegaard splittings of knot exteriors

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