# Stable loops and almost transverse surfaces

## TL;DR

This paper explores the duality between certain cones in hyperbolic 3-manifolds and minimal stable loops, providing new insights and a more accessible proof of Mosher's Transverse Surface Theorem.

## Contribution

It establishes a duality between cones over fibered faces and minimal stable loops, and offers a simplified proof of Mosher's theorem.

## Key findings

- Duality between cones and minimal stable loops
- New proof of Mosher's Transverse Surface Theorem
- Enhanced understanding of veering triangulations

## Abstract

We show that the cone over a fibered face of a compact fibered hyperbolic 3-manifold is dual to the cone generated by the homology classes of finitely many curves called minimal stable loops living in the associated veering triangulation. We also present a new, more hands-on proof of Mosher's Transverse Surface Theorem.