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Left-orderability, branched covers and double twist knots
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-13 , DOI: 10.1090/proc/15269 Hannah Turner
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-01-13 , DOI: 10.1090/proc/15269 Hannah Turner
Abstract:For some families of two-bridge knots, including double twist knots with genus at least four, we determine precisely the set of integers 
such that the fundamental group of the 
-fold cyclic branched cover of the 3-sphere along these knots is left-orderable. There are knots, including the figure-eight knot, for which this set is empty. We give the first class of hyperbolic knots, not of this type, for which these integers can be completely determined.
中文翻译：
左排序，分支覆盖和双扭结
摘要：对于某些两桥结的家族，包括至少四个属的双扭结，我们精确地确定了整数的集合，使得沿着这些结保留了3-球体的-折叠循环分支覆盖的基本群-可订购的。有一些打结，包括八字形打结，这套结是空的。我们给出第一类双曲型结，不是这种类型的双曲型结，可以完全确定这些整数。
更新日期：2021-02-08
such that the fundamental group of the -fold cyclic branched cover of the 3-sphere along these knots is left-orderable. There are knots, including the figure-eight knot, for which this set is empty. We give the first class of hyperbolic knots, not of this type, for which these integers can be completely determined. 中文翻译：
左排序，分支覆盖和双扭结
摘要：对于某些两桥结的家族，包括至少四个属的双扭结，我们精确地确定了整数的集合，
使得沿着这些结保留了3-球体的-折叠循环分支覆盖的基本群-可订购的。有一些打结，包括八字形打结，这套结是空的。我们给出第一类双曲型结，不是这种类型的双曲型结，可以完全确定这些整数。
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