Embedding non-arithmetic hyperbolic manifolds

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 $\le v$ that bounds geometrically is at least $v^{Cv}$, for $v$ large enough.

20 pages, 5 figures. Final version

References in corpus (2)

• Some hyperbolic three-manifolds that bound geometrically
• Quasi-arithmeticity of lattices in PO(n,1)

Cited by in corpus (1)

• The signature of cusped hyperbolic 4-manifolds