Genera of knots in the complex projective plane
Genera of knots in the complex projective plane
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复射影平面中的结属
DOI：
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发表时间：
2019
影响因子：
0.5
通讯作者：
Jacob Pichelmeyer
中科院分区：
文献类型：
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作者：
Jacob Pichelmeyer
我们的目标是系统地计算尽可能多的素数纽结的[公式：见正文]-亏格，最多8个交叉。我们通过相干带手术获得了[公式：见正文]-亏格的上界。我们得到的下限通过阻碍潜在的切片盘的同调度。障碍物是从低维拓扑中的各种来源中提取的，并适应[公式：见正文]。有27个素数结和不同的镜像多达7个交叉点。我们现在知道了所有这些结的[公式：见正文]-亏格。有64个素数结和不同的镜像多达8个交叉点。我们现在知道[公式：[公式：见正文]-属的所有这些结，但6个，其中[公式：见正文]-属没有明确确定，它被缩小到2种可能性。作为这项工作的结果，我们显示了一个无限的家庭的结，使[公式：见文字]-每个结的亏格不同于它的镜像。
Our goal is to systematically compute the [Formula: see text]-genus of as many prime knots up to 8-crossings as possible. We obtain upper bounds on the [Formula: see text]-genus via coherent band surgery. We obtain lower bounds by obstructing homological degrees of potential slice discs. The obstructions are pulled from a variety of sources in low-dimensional topology and adapted to [Formula: see text]. There are 27 prime knots and distinct mirrors up to 7-crossings. We now know the [Formula: see text]-genus of all of these knots. There are 64 prime knots and distinct mirrors up to 8-crossings. We now know the [Formula: see text]-genus of all but 6 of these knots, where the [Formula: see text]-genus was not determined explicitly, it was narrowed down to 2 possibilities. As a consequence of this work, we show an infinite family of knots such that the [Formula: see text]-genus of each knot differs from that of its mirror.
关于带状手术的注释和结的签名
影响因子：
0.9
作者：
Moore, Allison H.;Vazquez, Mariel
通讯作者：
Vazquez, Mariel