# Embedding arithmetic hyperbolic manifolds

## TL;DR

This paper proves that arithmetic hyperbolic n-manifolds of simplest type can be embedded into higher-dimensional hyperbolic manifolds or their mod 2 Abelian covers, advancing understanding of their geometric structures.

## Contribution

It establishes new embedding results for arithmetic hyperbolic manifolds of simplest type into higher dimensions or their covers.

## Key findings

- Arithmetic hyperbolic n-manifolds can embed into (n+1)-dimensional manifolds.
- Universal mod 2 Abelian covers also admit embeddings.
- Results apply specifically to manifolds of simplest type.

## Abstract

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.