# Essential loops in taut ideal triangulations

## TL;DR

This paper proves that in three-manifolds with taut ideal triangulations, all vertical or normal loops are essential, using a combinatorial approach based on Novikov's technique.

## Contribution

It introduces a combinatorial method to establish the essentiality of certain loops in taut ideal triangulations, extending Novikov's technique.

## Key findings

- Vertical or normal loops are essential in the fundamental group.
- The combinatorial approach simplifies the proof of essentiality.
- The result applies to three-manifolds with taut ideal triangulations.

## Abstract

In this note we combinatorialise a technique of Novikov. We use this to prove that, in a three-manifold equipped with a taut ideal triangulation, any vertical or normal loop is essential in the fundamental group.