Embedding non-arithmetic hyperbolic manifolds

Alexander Kolpakov; Stefano Riolo; Leone Slavich

doi:10.4310/mrl.2022.v29.n1.a7

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arXiv · 2003.01707

Embedding non-arithmetic hyperbolic manifolds

Alexander Kolpakov·Stefano Riolo·Leone Slavich

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Abstract

This paper shows that many hyperbolic manifolds obtained by glueing arithmetic pieces embed into higher-dimensional hyperbolic manifolds as codimension-one totally geodesic submanifolds. As a consequence, many Gromov--Pyatetski-Shapiro and Agol--Belolipetsky--Thomson non-arithmetic manifolds embed geodesically. Moreover, we show that the number of commensurability classes of hyperbolic manifolds with a representative of volume $\leq v$ that bounds geometrically is at least $v^{Cv}$, for $v$ large enough.

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BibTeX RIS

Alexander Kolpakov, Stefano Riolo, Leone Slavich. 2020-03-03. Embedding non-arithmetic hyperbolic manifolds. https://doi.org/10.4310/mrl.2022.v29.n1.a7

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