Distance one lens space fillings and band surgery on the trefoil knot
Distance one lens space fillings and band surgery on the trefoil knot
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DOI：
10.2140/agt.2019.19.2439
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发表时间：
2017-10
影响因子：
0.7
通讯作者：
Tye Lidman;Allison H. Moore;M. Vázquez
中科院分区：
文献类型：
--
作者：
Tye Lidman;Allison H. Moore;M. Vázquez
证明了如果透镜空间L（n，1）$是沿距离椭圆斜率为1的透镜空间L（3，1）$中的一个结点通过手术获得的，则n$在$\{-6，\pm 1，\pm 2，3，4，7\}$中.该结果产生了从三叶形到$T（2，n）$环面结和链接的相干和非相干带手术的分类。主要结果通过研究Heegaard Floer $d$-不变量在L（3，1）$中沿着纽结积分运算下的行为得到了证明.三叶形和环面结和链接之间的带状手术的分类是由自然界中的局部重连过程激发的，其被建模为带状手术。特别令人感兴趣的是环状DNA分子重组的研究。
We prove that if the lens space $L(n, 1)$ is obtained by a surgery along a knot in the lens space $L(3,1)$ that is distance one from the meridional slope, then $n$ is in $\{-6, \pm 1, \pm 2, 3, 4, 7\}$. This result yields a classification of the coherent and non-coherent band surgeries from the trefoil to $T(2, n)$ torus knots and links. The main result is proved by studying the behavior of the Heegaard Floer $d$-invariants under integral surgery along knots in $L(3,1)$. The classification of band surgeries between the trefoil and torus knots and links is motivated by local reconnection processes in nature, which are modeled as band surgeries. Of particular interest is the study of recombination on circular DNA molecules.