Embedding non-arithmetic hyperbolic manifolds

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.

Full Text (PDF format)

A.K. and S.R. were supported by the SNSF project no. PP00P2-170560.

Received 6 May 2020

Accepted 11 October 2020

Published 6 September 2022