The complete $10$-tetrahedra census of orientable cusped hyperbolic $3$-manifolds

TL;DR

This paper extends the census of orientable cusped hyperbolic 3-manifolds to 10 tetrahedra, providing detailed data on manifolds, triangulations, Dehn fillings, and a notable example with a totally geodesic surface.

Contribution

It presents the next comprehensive census of such manifolds, including new data, classifications, and a unique example with a totally geodesic surface.

Findings

Identified 150,730 new manifolds with 496,638 minimal ideal triangulations.

Cataloged 439,898 exceptional Dehn fillings.

Discovered the simplest orientable cusped hyperbolic 3-manifold with a closed totally geodesic surface.

Abstract

We extend the complete census of orientable cusped hyperbolic $3$-manifolds to $10$ tetrahedra, giving the next $150730$ manifolds and their $496638$ minimal ideal triangulations. As applications, we find the precisely $439898$ exceptional Dehn fillings on them, revealing the next $1849$ simplest hyperbolic knot exteriors in $S^3$. We also give the simplest example of an orientable cusped hyperbolic $3$-manifold containing a closed totally geodesic surface.