Non-left-orderable surgeries on twisted torus knots
Non-left-orderable surgeries on twisted torus knots
复制标题
扭曲环面结上的非左序手术
DOI：
10.1090/proc/12897
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Srikar Varadaraj
中科院分区：
文献类型：
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作者：
K. Christianson;J. Goluboff;L. Hamann;Srikar Varadaraj
博耶、戈登和沃森猜想，不可约有理同调3-球面是L-空间，当且仅当其基本群不是左可序的。由于大量的L-空间可以从3-球面中纽结的Dehn手术中产生，很自然地会问纽结群上的什么条件足以暗示与Dehn手术相关的商不是左可序的。Clay和沃森发展了一个判定此商群左可序性的准则，并用它验证了L-空间扭曲环面纽结上的外科手术猜想。我们推广了最近的定理Ichihara和Temma提供另一个这样的标准。然后，我们使用这个新的标准，推广的结果粘土和沃森，并验证了更广泛的一类L-空间扭曲环面结的猜想。
Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since large classes of L-spaces can be produced from Dehn surgery on knots in the 3-sphere, it is natural to ask what conditions on the knot group are sufficient to imply that the quotient associated to Dehn surgery is not left-orderable. Clay and Watson develop a criterion for determining the left-orderability of this quotient group and use it to verify the conjecture for surgeries on certain L-space twisted torus knots. We generalize a recent theorem of Ichihara and Temma to provide another such criterion. We then use this new criterion to generalize the results of Clay and Watson and to verify the conjecture for a much broader class of L-space twisted torus knots.