Mathematical Research Letters

Volume 25 (2018)

Number 4

Embedding arithmetic hyperbolic manifolds

Pages: 1305 – 1328



Alexander Kolpakov (Institut de Mathématiques, Université de Neuchâtel, Switzerland)

Alan W. Reid (Department of Mathematics, Rice University, Houston, Texas, U.S.A.)

Leone Slavich (Department of Mathematics, University of Pisa, Italy)


We prove that any arithmetic hyperbolic $n$-manifold of simplest type can either be geodesically embedded into an arithmetic hyperbolic $(n + 1)$-manifold or its universal $\mathrm{mod} \: 2$ Abelian cover can.

Received 14 April 2017

Accepted 8 October 2017

Published 16 November 2018