New hyperbolic 4-manifolds of low volume

TL;DR

This paper establishes the existence of multiple classes of minimal-volume hyperbolic 4-manifolds and constructs the smallest known non-arithmetic example using established techniques.

Contribution

It proves the existence of at least two commensurability classes of minimal-volume hyperbolic 4-manifolds and constructs the smallest known non-arithmetic hyperbolic 4-manifold.

Findings

At least 2 commensurability classes of minimal-volume hyperbolic 4-manifolds exist.

Constructed the smallest known non-arithmetic hyperbolic 4-manifold.

Provides new insights into the structure of hyperbolic 4-manifolds.

Abstract

We prove that there are at least 2 commensurability classes of minimal-volume hyperbolic 4-manifolds. Moreover, by applying a well-known technique due to Gromov and Piatetski-Shapiro, we build the smallest known non-arithmetic hyperbolic 4-manifold.