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arXiv 1610.04414math.GTmath.RT
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关于纽结群的高维表示

On high-dimensional representations of knot groups

Stefan Friedl, Michael Heusener

备注：
15 pages
发表信息：
Algebr. Geom. Topol. 18 (2018) 313-332
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摘要：

给定一个双曲纽结$K$和任何$n\geq 2$，阿贝尔表示和完整表示都在$\operatorname{SL}(n,\Bbb{C})$ -特征标簇中产生一个$(n-1)$ -维分量。维度$\geq n$的$\operatorname{SL}(n,\Bbb{C})$字符变体的组成部分称为高维。Cooper和Long证明了在$\operatorname{SL}(2,\Bbb{C})$ -特征标簇中存在具有高维分量的双曲纽结。我们表明，任何非平凡的结$K$和足够大的$n$的$\operatorname{SL}(n,\Bbb{C})$字符品种的$K$承认高维组件。

英文摘要：

Given a hyperbolic knot $K$ and any $n\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\operatorname{SL}(n,\Bbb{C})$-character variety. A component of the $\operatorname{SL}(n,\Bbb{C})$-character variety of dimension $\geq n$ is called high-dimensional. It was proved by Cooper and Long that there exist hyperbolic knots with high-dimensional components in the $\operatorname{SL}(2,\Bbb{C})$-character variety. We show that given any non-trivial knot $K$ and sufficiently large $n$ the $\operatorname{SL}(n,\Bbb{C})$-character variety of $K$ admits high-dimensional components.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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