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.File | Dimensione | Formato | |
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