Collar parameters for Teichmuller Space & Measured Foliations on a Surface Research Announcement

TL;DR

This paper introduces a novel coordinate system for Teichmuller space that aligns the Thurston compactification with Euclidean radial compactification, enhancing understanding of surface moduli.

Contribution

It proposes a new coordinate framework for Teichmuller space that simplifies the Thurston compactification process.

Findings

New coordinates for Teichmuller space established

Thurston compactification shown as Euclidean radial compactification

Enhanced geometric understanding of surface moduli

Abstract

We defined a new set of coordinates with respect to which the Thurston compactification of Teichmuller space is the radial compactification of Euclidean space.