Counting cusped hyperbolic 3-manifolds that bound geometrically

TL;DR

This paper demonstrates that the count of cusped hyperbolic 3-manifolds bounding geometrically increases at a super-exponential rate relative to their volume, applicable to both arithmetic and non-arithmetic cases.

Contribution

It establishes a super-exponential growth rate for the number of such manifolds, expanding understanding of their distribution and complexity.

Findings

Number of manifolds grows super-exponentially with volume

Growth applies to both arithmetic and non-arithmetic manifolds

Provides quantitative bounds on manifold counts

Abstract

We show that the number of isometry classes of cusped hyperbolic $3$-manifolds that bound geometrically grows at least super-exponentially with their volume, both in the arithmetic and non-arithmetic settings.