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 vCv, for v large enough.

Embedding non-arithmetic hyperbolic manifolds

Riolo, Stefano;Slavich, Leone
2022-01-01

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 vCv, for v large enough.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1461825
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