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Geometry, topology and dynamics of character varieties

Autor: William Goldman; Caroline Series; Ser Peow Tan
Editora: Hackensack, N.J. : World Scientific, 2012.
Séries: Lecture notes series (National University of Singapore. Institute for Mathematical Sciences), v. 23.
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Resumo:
This volume is based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010. Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is  Ler mais...
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Gênero/Forma: Electronic books
Formato Físico Adicional: Print version:
Goldman, William.
Geometry, Topology and Dynamics of Character Varieties.
Singapore : World Scientific, ©2012
Tipo de Material: Recurso Internet
Tipo de Documento: Recurso Internet, Arquivo de Computador
Todos os Autores / Contribuintes: William Goldman; Caroline Series; Ser Peow Tan
ISBN: 9789814401364 9814401366 1281603678 9781281603678
Número OCLC: 808340709
Descrição: 1 online resource (xi, 349 p. :) ill.
Conteúdos: Foreword; Preface; An Invitation to Elementary Hyperbolic Geometry Ying Zhang; Introduction; 1. Euclid's Elements, Book I and Neutral Plane Geometry; 1.1. A brief review of contents of Elements, Book I; 1.2. A useful lemma; 1.3. A gure-free proof of Proposition I.7; 1.4. More notes on Elements, Book I; 1.5. Playfair's axiom; 1.6. Neutral plane geometry; 1.7. Angle-sums of triangles and Legendre's Theorems; 1.8. Quadrilaterals with two consecutive right angles; 1.9. Saccheri and Lambert quadrilaterals; 1.10. Variation of triangles in a neutral plane. 1.11. A midline configuration for triangles1.12. More theorems of neutral plane geometry; 1.13. Small angles; 2. Hyperbolic Plane Geometry; 2.1. Hyperbolic plane; 2.2. Asymptotic Parallelism; 2.3. Angle of parallelism; 2.4. The variation in the distance between two straight lines; 2.5. Some more theorems in hyperbolic plane geometry; 2.6. Construction of the common perpendicular to two ultra-parallel straight lines; 2.7. Construction of asymptotic parallels; 2.8. Ideal points; 2.9. Horocycles; 2.10. Construction of the straight line joining two given ideal points; 2.11. Ultra-ideal points. 2.12. The projective plane associated to a hyperbolic plane2.13. Center-pencils of a hyperbolic triangle; 2.14. Equidistant curves; 2.15. Positions of proper points relative to an ideal point; 2.16. Hyperbolic areas via equivalence of triangles; 2.17. Metric relations of corresponding arcs in concentric horocycles; 3. Isometries of the Hyperbolic Plane; 3.1. Isometries and reections in straight lines; 3.2. Orientation preserving/reversing isometries; 3.3. Rotations; 3.4. Translations; 3.5. Isometries of parabolic type; 3.6. Redundancy of two reflections. 3.7. Orientation reversing isometries as reflections and glide reflections3.8. Isometries as projective transformations; 3.9. Invariant projective lines of; 3.10. Composition of two orientation preserving isometries other than two translations; 3.11. Composition of two translations; 3.12. Conjugates of isometries; 3.13. The orthic triangle; 4. Hyperbolic Trigonometry Derived from Isometries; 4.1. Some identities of isometries of a neutral plane; 4.2. Some trigonometric formulas in H2(k); 4.3. Upper half-plane model U2 for hyperbolic plane H2(1); 4.4. Matrices of certain isometries of U2. 4.5. Trigonometric laws via identities of isometries4.6. Suggested further readings; Acknowledgments; References; Hyperbolic Structures on Surfaces Javier Aramayona; 1. Introduction; 2. Plane Hyperbolic Geometry; 2.1. Mobius transformations; 2.1.1. Classification in terms of trace and fixed points; 2.2. Models for hyperbolic geometry; 2.2.1. Hyperbolic distance; 2.2.2. Mobius transformations act by isometries; 2.2.3. The Cayley transformation; 2.2.4. Hyperbolic geodesics; 2.2.5. The boundary at infinity; 2.2.6. The full isometry group; 2.2.7. Dynamics of elements of Isom+(H).
Título da Série: Lecture notes series (National University of Singapore. Institute for Mathematical Sciences), v. 23.
Responsabilidade: editors, William Goldman, Caroline Series, Ser Peow Tan.

Resumo:

Based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for  Ler mais...

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