# Essential closed surfaces and finite coverings of negatively curved cusped 3-manifolds

## TL;DR

This paper proves that finite coverings of certain negatively curved, cusped 3-manifolds with ideal triangulations contain essential closed surfaces, advancing understanding of their topological structure.

## Contribution

It establishes the existence of essential closed surfaces in finite covers of negatively curved cusped 3-manifolds with ideal triangulations.

## Key findings

- Essential closed surfaces exist in finite covers of these manifolds.
- The manifolds admit a regular, negatively curved, ideal structure.
- The result applies to manifolds triangulated by finitely many ideal tetrahedra.

## Abstract

The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.