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 ≤v that bounds geometrically is at least v^Cv, for v large enough.

Kolpakov, A., Riolo, S., Slavich, L. (2022). Embedding non-arithmetic hyperbolic manifolds. MATHEMATICAL RESEARCH LETTERS, 29(1), 247-274 [10.4310/MRL.2022.v29.n1.a7].

Embedding non-arithmetic hyperbolic manifolds

Riolo, Stefano;Slavich, Leone
2022

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 ≤v that bounds geometrically is at least v^Cv, for v large enough.
2022
Kolpakov, A., Riolo, S., Slavich, L. (2022). Embedding non-arithmetic hyperbolic manifolds. MATHEMATICAL RESEARCH LETTERS, 29(1), 247-274 [10.4310/MRL.2022.v29.n1.a7].
Kolpakov, Alexander; Riolo, Stefano; Slavich, Leone
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/893618
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