EQUIVALENCE OF SYMMETRIC UNION DIAGRAMS
EQUIVALENCE OF SYMMETRIC UNION DIAGRAMS
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对称联合图的等价
DOI：
10.1142/s0218216507005555
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发表时间：
2007
影响因子：
0.5
通讯作者：
C. Lamm
中科院分区：
文献类型：
--
作者：
Michael Eisermann;C. Lamm
受丝带结研究的启发，我们探索了对称结，这是木下和寺阪50年前提出的一种美丽的结构。很容易看出，每个对称联合都代表一个缎带结，但其逆仍然是一个开放的问题。除了存在之外，考虑唯一性问题也是很自然的。为了解决这个问题，我们将通常的Reidemeister移动扩展到尊重对称性的一系列移动，并考虑由此产生的对称等价。有了这个概念，我们讨论了结可以具有本质上不同的对称并表示的几种情况。我们展示了一个无限家族的带状双桥结，每个都允许两种不同的对称联合表示。
Motivated by the study of ribbon knots we explore symmetric unions, a beautiful construction introduced by Kinoshita and Terasaka 50 years ago. It is easy to see that every symmetric union represents a ribbon knot, but the converse is still an open problem. Besides existence it is natural to consider the question of uniqueness. In order to attack this question we extend the usual Reidemeister moves to a family of moves respecting the symmetry, and consider the symmetric equivalence thus generated. This notion being in place, we discuss several situations in which a knot can have essentially distinct symmetric union representations. We exhibit an infinite family of ribbon two-bridge knots each of which allows two different symmetric union representations.