# Chapter Thirteen: Proof of the HST

## Related Articles

- Chapter One: Introduction. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p3
Chapter 1 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It explores the mathematical theory that includes Dehn filling and Thurston's theorem. Further it explores the horotube surgery theorem, and spherical CR structures. It highlights that...

- Chapter Four: Reflection Triangle Groups. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p32
Chapter 4 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It introduces the reflection triangle groups that is related to the Horotube Surgery Theorem (HST). It also describes the simplest complex reflection triangle groups. Further it also describes...

- Chapter Seven: Transplanting Horotube Functions. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p56
Chapter 7 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It uses the Siegel model that feed into the proof of the High School Transcript Studies (HST). Further it uses several mathematical model to proof the Transplant Lemma. It also deals with basic...

- Chapter Ten: Constructing the Boundary Complex. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p72
Chapter 10 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It defines the horotube complex and control its geometry and topology and deals with collections of horotubes and their functions. It uses horotube group that has a horotube function...

- Chapter Fifteen: Cusp Flexibility. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p113
Chapter 15 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It uses the Cusp Flexibility Lemma to prove mathematical theorem. It also gives an elementary and self-contained proof of Cusp Flexibility Lemma. Further it provides the Multiplicity of the...

- Chapter Two: Rank-One Geometry. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p12
Chapter 2 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It provides background material on complex hyperbolic geometry. Further it discusses several mathematical model including Klein Model, PoincarÃ© Model, and Upper Half-Space Model. It also...

- Chapter Three: Topological Generalities. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p23
Chapter 3 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It provides background material on discrete groups and topology. It describes a model for the singular space, and foundational material on complex hyperbolic discrete groups. Further it...

- Chapter Five: Heuristic Discussion of Geometric Filling. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p41
Chapter 5 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It presents a dictionary that translates between certain spherical CR objects and real hyperbolic objects. Further it mentions that there are perturbations of the hyperbolic structure to...

- Chapter Six: Extending Horotube Functions. // Spherical CR Geometry & Dehn Surgery;2007, Issue 165, p53
Chapter 6 of the book "Spherical CR Geometry and Dehn Surgery," by Richard Evan Schwartz is presented. It presents a technical results that feed into the proof of the High School Transcript Studies (HST). It also deal with basic properties of individual horotubes and their functions that defines...