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arXiv · 2003.05427

Embedding closed totally geodesic surfaces in Bianchi orbifolds

Junehyuk Jung·Alan W. Reid
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Abstract

We study embedding of closed totally geodesic hyperbolic 2-orbifolds in the Bianchi orbifolds $\mathbb{H}^3/PSL(2,\mathcal{O}_d)$. Our main result shows that there is a constant $c$ such that for $d$ large enough there are at least $cd$ closed embedded totally geodesic hyperbolic 2-orbifolds. Moreover we provide a list which conjecturally consists of those $d$ for which $\mathbb{H}^3/PSL(2,\mathcal{O}_d)$ does not contain a closed embedded totally geodesic hyperbolic 2-orbifold.

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Junehyuk Jung, Alan W. Reid. 2020-03-11. Embedding closed totally geodesic surfaces in Bianchi orbifolds. https://arxiv.org/abs/2003.05427

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