Genus 2 Cantor sets

Alastair N. Fletcher; Daniel Stoertz

doi:10.2140/pjm.2022.321.283

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arXiv · 2009.12427

Genus 2 Cantor sets

Alastair N. Fletcher·Daniel Stoertz

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Abstract

We construct a geometrically self-similar Cantor set $X$ of genus $2$ in $\mathbb{R}^3$. This construction is the first for which the local genus is shown to be $2$ at every point of $X$. As an application, we construct, also for the first time, a uniformly quasiregular mapping $f:\mathbb{R}^3 \to \mathbb{R}^3$ for which the Julia set $J(f)$ is a genus $2$ Cantor set.

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BibTeX RIS

Alastair N. Fletcher, Daniel Stoertz. 2020-09-25. Genus 2 Cantor sets. https://doi.org/10.2140/pjm.2022.321.283

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