Knot graphs and Gromov hyperbolicity

被引：0
作者：
Stanislav Jabuka
Beibei Liu
Allison H. Moore
机构：
[1] University of Nevada,Department of Mathematics and Statistics
[2] Georgia Institute of Technology,School of Mathematics
[3] Virginia Commonwealth University,Department of Mathematics and Applied Mathematics
来源：
Mathematische Zeitschrift | 2022年 / 301卷
关键词：
Knots; Unknotting operations; Gromov hyperbolicity; 57K10; 57K18;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We define a broad class of graphs that generalize the Gordian graph of knots. These knot graphs take into account unknotting operations, the concordance relation, and equivalence relations generated by knot invariants. We prove that overwhelmingly, the knot graphs are not Gromov hyperbolic, with the exception of a particular family of quotient knot graphs. We also investigate the property of homogeneity, and prove that the concordance knot graph is homogeneous. Finally, we prove that that for any n, there exists a knot K such that the ball of radius n in the Gordian graph centered at K contains no connected sum of torus knots.
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页码：811 / 834
页数：23
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