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A shorter note on shorter pants

Hugo Parlier

Abstract

This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.

A shorter note on shorter pants

Abstract

This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.
Paper Structure (3 sections, 4 theorems, 7 equations, 3 figures)

This paper contains 3 sections, 4 theorems, 7 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. Proof of Theorem \ref{['thm:intro']}

Key Result

Theorem 1.1

Let $X$ be a hyperbolic surface, possibly with geodesic boundary, and of finite area. Then $X$ admits a pants decomposition where each curve is of length at most

Figures (3)

  • Figure 1: The paths $c$ and $h$
  • Figure 2: The hexagon and pentagons in the second case
  • Figure 3: The two topological types for the path

Theorems & Definitions (6)

  • Theorem 1.1
  • Lemma 2.1: Length expansion lemma
  • Lemma 2.2
  • proof
  • Lemma 3.1
  • proof