A connected string of long thick and dominants

TL;DR

This paper proves that Teichmuller geodesics contain a sequence of long, thick, and dominant segments with bounded gaps, enabling results analogous to hyperbolic geodesics and impacting hyperbolic three-manifold geometry.

Contribution

It introduces a novel structural property of Teichmuller geodesics, linking their segments to hyperbolic geometry applications.

Findings

Existence of a string of intersecting long, thick, dominant segments in Teichmuller geodesics

Bounded distance between consecutive segments

Applications to hyperbolic three-manifold geometry

Abstract

We prove that every Teichmuller geodesic of a finite type surface contains a string of intersecting long, thick and dominant segments, such that the distance between consecutive segments is bounded. This is key to obtaining some results about Teichmuller geodesics which mimic those for hyperbolic geodesics. These results have important applications to results about the geometry of hyperbolic three-manifolds.