# Two-Generator Discrete Subgoups of \(PSL(2, R)\)

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*Jane Gilman*

#### Table of Contents

# Table of Contents

## Two-Generator Discrete Subgoups of $PSL(2, R)$

- Contents v6 free
- I: Introduction 112 free
- 1 Introduction 314 free
- 2 The Acute Triangle Theorem 1324
- 2.1 Nielsen equivalence 1324
- 2.2 Idea of proof: Acute triangle theorem 1930
- 2.3 Labeling Conventions 2031
- 2.4 Ascending order conventions 2132
- 2.5 The Triangle Algorithm 2132
- 2.6 Q and the last triangle along A 2536
- 2.7 Combining triangle algorithm steps 2839
- 2.8 The sides and heights converge to 0 3142
- 2.9 Acute triangle theorem: proof 3142

- 3 Discreteness Theorem Proof Outline 3344

- II: Preliminaries 3950
- III: Geometric Equivalence and the Discreteness Theorem 95106
- IV: The Real Number Algorithm and the Turing Machine Algorithm 165176
- V: Appendix 193204