Weil-Petersson geometry of Teichmuller-Coxeter complex and its finite rank property

TL;DR

This paper constructs a Weil-Petersson geodesic completion of Teichmuller space using Coxeter complex formalism, revealing a finite rank property similar to symmetric spaces of Lie groups.

Contribution

It introduces a novel Coxeter complex approach to Teichmuller space, establishing finite rank properties in its metric and geodesic completions.

Findings

The geodesic completion satisfies a finite rank property.

The metric completion shares the finite rank characteristic.

Similarity to non-compact symmetric spaces is demonstrated.

Abstract

We construct a Weil-Petersson geodesic completion of Teichmuller space through the formalism of Coxeter complex with the Teichmuller space as its non-linear non-homogeneous fundamental domain. We show that the metric and geodesic completions both satisfy a finite rank property, demonstrating a similarity with the non-compact symmetric spaces of semi-simple Lie groups.