具有任意编织指数的非对称L空间纽结
Asymmetric L-space knots with arbitrary braid index
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中文总结 AI 辅助
本文构造了任意编织指数大于4的非对称双曲L空间纽结，且对每个指数均存在无穷多个，推广了Baker等人的结果。
中文摘要 AI 辅助
Baker和Luecke首次发现了非对称L空间纽结的例子。在Baker-Luecke纽结中，最简单的一个具有编织指数12。后来发现，在SnapPy普查中仅有9个非对称双曲L空间纽结，其编织指数取值分别为4、5、6和7。已知非对称L空间纽结的编织指数至少为4。最近，Baker和本文第二作者构造了无穷多个编织指数为4的非对称双曲L空间纽结。本文构造了一个编织指数大于4的任意值的非对称双曲L空间纽结。事实上，对于每个编织指数，都存在无穷多个这样的纽结。
英文摘要
The first examples of asymmetric L-space knots were found by Baker and Luecke. Among Baker-Luecke knots, the simplest one has braid index 12. Later, it turned out that there are just 9 asymmetric hyperbolic L-space knots in the SnapPy census, and their braid indices take the values 4, 5, 6 and 7. It is known that asymmetric L-space knots have braid index at least 4. Recently, Baker and the second author give infinitely many asymmetric hyperbolic L-space knots with braid index 4. In this paper, we construct an asymmetric hyperbolic L-space knot with arbitrary braid index bigger than 4. In fact, there exist infinitely many such knots for each braid index.
发表机构
- Yamaguchi University（山口大学）
- Hiroshima University（广岛大学）
机构由 AI 辅助整理，请以论文原文为准。
