Dynamical aspects of teichmüller theory : SL(2, R)-action on moduli spaces of flat surfaces /: SL(2, R)-action on moduli spaces of flat surfaces. ([2018])

• Record Type: Book
• Further Information: Note: Carlos Matheus Silva Santos.
• Authors: Santos, Carlos Matheus Silva
• Contents: Intro; Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Abelian Differentials and Their Moduli Spaces; 1.2 Translation Structures; 1.3 Some Examples of Translation Surfaces; 1.3.1 Abelian Differentials on Complex Torus; 1.3.2 Square-Tiled Surfaces; 1.3.3 Suspensions of Interval Exchange Transformations; 1.3.4 Billiards in Rational Polygons; 1.4 Stratification of Moduli Spaces of Translation Surfaces; 1.5 Period Coordinates; 1.6 Connected Components of Strata; 1.7 GL+(2, mathbbR) Action on mathcalHg; 1.8 SL(2, mathbbR)-Action on mathcalHg. 1.9 Teichmüller Flow and Kontsevich-Zorich Cocycle1.10 Teichmüller Curves, Veech Surfaces and Affine Homeomorphisms; 2 Proof of the Eskin-Kontsevich-Zorich Regularity Conjecture; 2.1 Eskin-Kontsevich-Zorich Formula; 2.2 Statement of the Eskin-Kontsevich-Zorich Regularity Conjecture; 2.3 Idea of the Proof of Theorem 9; 2.4 Reduction of Theorem 9 to Propositions 14 and 15; 2.5 Proof of Proposition 14 (Modulo Propositions 16 and 17); 2.6 Proof of Proposition 15 (Modulo Proposition 16); 2.7 Proof of Proposition 16 via Rokhlin's Disintegration Theorem. 2.8 Proof of Proposition 17 via Rokhlin's Disintegration Theorem3 Arithmetic Teichmüller Curves with Complementary Series; 3.1 Exponential Mixing of the Teichmüller Flow; 3.2 Teichmüller Curves with Complementary Series; 3.3 Idea of Proof of Theorem 40; 3.4 Quick Review of Representation Theory of SL(2, mathbbR); 3.4.1 Spectrum of Unitary SL(2, mathbbR)-Representations; 3.4.2 Bargmann's Classification; 3.4.3 Hyperbolic Surfaces and Examples of Regular Unitary SL(2, mathbbR)-Representations; 3.4.4 Rates of Mixing and Spectral Gap. 5.2 Lyapunov Exponents of Teichmüller Curves and Random Products of Matrices5.3 Galois-Theoretical Criterion for Simplicity of Exponents of Origamis; 5.3.1 Galois-Pinching Matrices; 5.3.2 Twisting with Respect to Galois-Pinching Matrices I: Statements of Results; 5.3.3 Twisting with Respect to Galois-Pinching Matrices II: Proof of Theorem 67; 5.3.4 Two Simplicity Criteria for the Lyapunov Exponents of Origamis; 5.4 A Counterexample to an Informal Conjecture of Forni; 6 An Example of Quaternionic Kontsevich-Zorich Monodromy Group.
• Publisher Details: Cham [Amsterdam] : Springer Atlantis Press
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 531.11; Mathematics; Dynamics; Teichmüller spaces; Geometry; Moduli theory; SCIENCE -- Mechanics -- General; SCIENCE -- Mechanics -- Solids; Dynamics; Geometry; Moduli theory; Teichmüller spaces; Mathematics; Dynamical Systems and Ergodic Theory; Algebraic Geometry; Topology; Mathematics -- Geometry -- Algebraic; Mathematics -- Topology; Algebraic geometry; Topology; Differentiable dynamical systems; Geometry, algebraic; Topology; Mathematics -- Mathematical Analysis; Nonlinear science; Electronic books
• Languages: English
• ISBNs: 9783319921594; 3319921592; 3319921584; 9783319921587
• Related ISBNs: 9783319921587; 3319921584
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed July 16, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.