大 Heegaard 属的小结

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2023-12-06 DOI:10.4310/cag.2023.v31.n2.a6

William Worden

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引用次数: 0

摘要

根据阿戈尔提出的观点，我们构建了一个双曲结$K_n$族，其补集不包含闭合不可压缩曲面，且希嘉属恰好为$n$。这是已知的第一个此类结的例子。利用 Futer 和 Purcell 的研究成果，我们可以用 $n$ 约束每个 $K_n$ 的交叉数。

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Small knots of large Heegaard genus

Building off ideas developed by Agol, we construct a family of hyperbolic knots $K_n$ whose complements contain no closed incompressible surfaces and have Heegaard genus exactly $n$. These are the first known examples of small knots having large Heegaard genus. Using work of Futer and Purcell, we are able to bound the crossing number for each $K_n$ in terms of $n$.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.