Foundations of Hyperbolic Manifolds, Third Edition (3rd Ed) (Instructor Solution Manual, Solutions)

✍ Scribed by John G. Ratcliffe

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 341
• Series: Graduate Texts in Mathematics, 149
• Edition: 3, 3e
• Category: Library

✦ Synopsis

obtained thanks to https://t.me/HermitianSociety

✦ Table of Contents

Euclidean Geometry
Euclid's Parallel Postulate
Independence of the Parallel Postulate
Euclidean n-Space
Geodesics
Arc Length
Spherical Geometry
Spherical n-Space
Elliptic n-Space
Spherical Arc Length
Spherical Volume
Spherical Trigonometry
Hyperbolic Geometry
Lorentzian n-Space
Hyperbolic n-Space
Hyperbolic Arc Length
Hyperbolic Volume
Hyperbolic Trigonometry
Inversive Geometry
Reflections
Stereographic Projection
Möbius Transformations
Poincaré Extension
The Conformal Ball Model
The Upper Half-Space Model
Classification of Transformations
Isometries of Hyperbolic Space
Topological Groups
Groups of Isometries
Discrete Groups
Discrete Euclidean Groups
Elementary Groups
Geometry of Discrete Groups
The Projective Disk Model
Convex Sets
Convex Polyhedra
Geometry of Convex Polyhedra
Polytopes
Fundamental Domains
Convex Fundamental Polyhedra
Tessellations
Classical Discrete Groups
Reflection Groups
Simplex Reflection Groups
Generalized Simplex Reflection Groups
The Volume of a Simplex
Crystallographic Groups
Torsion-Free Linear Groups
Geometric Manifolds
Geometric Spaces
Clifford-Klein Space-Forms
(X,G)-Manifolds
Developing
Completeness
Geometric Surfaces
Compact Surfaces
Gluing Surfaces
The Gauss-Bonnet Theorem
Moduli Spaces
Closed Euclidean Surfaces
Closed Geodesics
Closed Hyperbolic Surfaces
Hyperbolic Surfaces of Finite Area
Hyperbolic 3-Manifolds
Gluing 3-Manifolds
Complete Gluing of 3-Manifolds
Finite Volume Hyperbolic 3-Manifolds
Hyperbolic Volume
Hyperbolic Dehn Surgery
Hyperbolic n-Manifolds
Gluing n-Manifolds
Poincaré's Theorem
The Gauss-Bonnet Theorem
Simplices of Maximum Volume
Differential Forms
Simplicial Volume
Measure Homology
Mostow Rigidity
Geometrically Finite n-Manifolds
Limit Sets
Limit Sets of Discrete Groups
Limit Points
Geometrically Finite Discrete Groups
Nilpotent Groups
The Margulis Lemma
Geometrically Finite Manifolds
Arithmetic Hyperbolic Groups
Geometric Orbifolds
Orbit Spaces
(X,G)-Orbifolds
Developing Orbifolds
Gluing Orbifolds
Poincaré's Theorem