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In the tradition of Thurston II : geometry and groups / / Ken'ichi Ohshika, Athanase Papadopoulos, editors
In the tradition of Thurston II : geometry and groups / / Ken'ichi Ohshika, Athanase Papadopoulos, editors
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (525 pages)
Disciplina 516
Soggetto topico Geometry
Group theory
Geometria
Teoria de grups
Soggetto genere / forma Llibres electrònics
ISBN 3-030-97560-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 2 A Survey of Complex Hyperbolic Kleinian Groups -- 2.1 Introduction -- 2.2 Complex Hyperbolic Space -- 2.3 Basics of Discrete Subgroups of PU(n,1) -- 2.4 Margulis Lemma and Thick-Thin Decomposition -- 2.5 Geometrically Finite Groups -- 2.6 Ends of Negatively Curved Manifolds -- 2.7 Critical Exponent -- 2.8 Examples -- 2.9 Complex Hyperbolic Kleinian Groups and Function Theory on Complex Hyperbolic Manifolds -- 2.10 Conjectures and Questions -- Appendix A: Horofunction Compactification -- Appendix B: Two Classical Peano Continua -- Appendix C: Gromov-Hyperbolic Spaces and Groups -- Appendix D: Orbifolds -- Appendix E: Ends of Spaces -- Appendix F: Generalities on Function Theory on Complex Manifolds -- Appendix G (by Mohan Ramachandran): Proof of Theorem 2.19 -- References -- 3 Möbius Structures, Hyperbolic Ends and k-Surfaces in Hyperbolic Space -- 3.1 Overview -- 3.1.1 Hyperbolic Ends and Möbius Structures -- 3.1.2 Infinitesimal Strict Convexity, Quasicompleteness and the Asymptotic Plateau Problem -- 3.1.3 Schwarzian Derivatives -- 3.1.4 Closing Remarks and Acknowledgements -- 3.2 Möbius Structures -- 3.2.1 Möbius Structures -- 3.2.2 The Möbius Disk Decomposition and the Join Relation -- 3.2.3 Geodesic Arcs and Convexity -- 3.2.4 The Kulkarni-Pinkall Form -- 3.2.5 Analytic Properties of the Kulkarni-Pinkall Form -- 3.3 Hyperbolic Ends -- 3.3.1 Hyperbolic Ends -- 3.3.2 The Half-Space Decomposition -- 3.3.3 Geodesic Arcs and Convexity -- 3.3.4 Ideal Boundaries -- 3.3.5 Extensions of Möbius Surfaces -- 3.3.6 Left Inverses and Applications -- 3.4 Infinitesimally Strictly Convex Immersions -- 3.4.1 Infinitesimally Strictly Convex Immersions -- 3.4.2 A Priori Estimates -- 3.4.3 Cheeger-Gromov Convergence -- 3.4.4 Labourie's Theorems and Their Applications -- 3.4.5 Uniqueness and Existence.
Appendix A: A Non-complete k-Surface -- Appendix B: Category Theory -- References -- 4 Cone 3-Manifolds -- 4.1 Introduction -- 4.2 Cone Manifolds -- 4.3 Hyperbolic Dehn Filling -- 4.4 Local Rigidity -- 4.5 Sequences of Cone Manifolds -- 4.5.1 Compactness Theorem -- 4.5.2 Cone-Thin Part -- 4.5.3 Decreasing Cone Angles: Global Rigidity -- 4.5.4 Increasing Cone Angles -- 4.6 Examples -- 4.6.1 Hyperbolic Two-Bridge Knots and Links -- 4.6.2 Montesinos Links -- 4.6.3 A Cusp Opening -- 4.6.4 Borromean Rings -- 4.6.5 Borromean Rings Revisited: Spherical Structures -- References -- 5 A Survey of the Thurston Norm -- 5.1 Introduction -- Organization -- Conventions and Notation -- 5.2 Foundations of the Thurston Norm -- 5.2.1 Thurston Norm -- 5.2.2 Norm Balls and Fibrations Over a Circle -- 5.2.3 Norm-Minimizing Surfaces and Codimension-1 Foliations -- 5.2.4 Singular and Gromov Norms -- 5.3 Alexander and Teichmüller Polynomials -- 5.3.1 Alexander Polynomial -- 5.3.2 Abelian Torsion -- 5.3.3 Teichmüller Polynomial -- 5.4 Seiberg-Witten Invariant -- 5.4.1 Seiberg-Witten Theory -- 5.4.2 Seiberg-Witten Invariant of a 3-Manifold -- 5.4.3 Complexity of Surfaces in a 4-Manifold -- 5.4.4 Harmonic Norm -- 5.5 Floer Homology -- 5.5.1 Heegaard Floer Homology -- 5.5.2 Knot Floer Homology -- 5.6 Torsion Invariants -- 5.6.1 Reidemeister Torsion -- 5.6.2 Twisted Alexander Polynomials -- 5.6.3 Higher-Order Alexander Polynomials -- 5.6.4 L2-Alexander Torsion -- 5.7 Triangulations -- 5.7.1 Thurston Norm Via Normal Surfaces -- 5.7.2 Z / 2 Z-Thurston Norm and Complexity of 3-Manifolds -- 5.8 Profinite Rigidity -- 5.9 Conjectures and Questions -- 5.9.1 Realization Problem -- 5.9.2 Complexity Functions for Circle Bundles -- 5.9.3 Twisted Alexander Polynomials for Hyperbolic Knots -- 5.9.4 Higher-Order Alexander Polynomials and the Knot Genus.
5.9.5 Lower Bounds on Complexity of 3-Manifolds -- 5.9.6 Thurston Norm Balls of Finite Covers -- References -- 6 From Hyperbolic Dehn Filling to Surgeries inRepresentation Varieties -- 6.1 Introduction -- 6.2 Hyperbolic Dehn Surgery -- 6.2.1 Dehn Surgery -- 6.2.2 Hyperbolic Dehn Surgery -- 6.2.3 Haken Manifolds and Thurston's Uniformization -- 6.3 Deformations of Hyperbolic Structures by Bending -- 6.4 Higher Teichmüller Theory -- 6.4.1 The Teichmüller Space -- 6.4.2 Higher Teichmüller Spaces -- 6.4.3 -Positive Representations -- 6.5 Non-abelian Hodge Theory -- 6.5.1 Moduli Spaces of G-Higgs Bundles -- 6.5.2 G-Hitchin Equations -- 6.5.3 The Non-abelian Hodge Correspondence -- 6.6 Surgeries in Representation Varieties-General Theory -- 6.6.1 Topological Gluing Construction -- 6.6.2 Gluing in Exceptional Components of the Moduli Space -- 6.6.2.1 Parabolic GL( n,C )-Higgs Bundles -- 6.6.3 Complex Connected Sum of Riemann Surfaces -- 6.6.4 Gluing at the Level of Solutions to Hitchin's Equations -- 6.6.4.1 The Local Model -- 6.6.4.2 Approximate Solutions of the SL(2,R)-Hitchin Equations -- 6.6.5 Approximate Solutions to the G-Hitchin Equations -- 6.6.6 The Contraction Mapping Argument -- 6.6.7 Correcting an Approximate Solution to an Exact Solution -- 6.6.8 Topological Invariants -- 6.7 Examples: Model Higgs Bundles in Exceptional Components of Orthogonal Groups -- 6.7.1 SO( p,q )-Higgs Bundle Data -- 6.7.2 Hitchin Equations for Orthogonal Groups -- 6.7.3 Model Parabolic SL( 2,R )-Higgs Bundles -- 6.7.4 Parabolic SO( p,p+1 )-Models -- 6.7.4.1 Models via the Irreducible Representation SL( 2,R )-3muSO( p,p+1 ) -- 6.7.4.2 Models via the General Map -- 6.7.5 Gauge-Theoretic Gluing of Parabolic SO( p,p+1 )-Higgs Bundles -- 6.7.6 Model Representations in the Exceptional Components of R( SO( p,p+1 ) ) -- 6.7.7 Model Representations and Positivity -- References.
7 Acute Geodesic Triangulations of Manifolds -- 7.1 Introduction -- 7.2 In Dimension Three and Higher -- 7.2.1 Polytopes and Dehn-Sommerville Equations -- 7.2.2 Spherical Complexes -- 7.2.3 Dimension Four and Five -- 7.2.4 R3, S3 and More -- 7.3 Dimension Two: General Riemannian and Flat Cone Metrics -- 7.3.1 Riemannian Surfaces -- 7.3.2 Euclidean and Flat Cone Surfaces -- 7.3.3 Parametrizing Equilateral Triangulations -- 7.3.4 Aperiodic Tilings -- 7.4 Round Spheres -- 7.4.1 Acute Triangulations from Right-Angled Hyperbolic 3-Polytopes -- 7.4.2 The Koebe-Andreev-Thurston Theorem and Its Generalizations -- 7.4.3 CAT(κ) Spaces -- References -- 8 Signature Calculation of the Area Hermitian Form on Some Spaces of Polygons -- 8.1 Introduction -- 8.2 Basic Facts on Hermitian Forms -- 8.3 Spaces of Polygons and Signature Calculation -- 8.3.1 The Area Hermitian Form and the Formula for Its Signature -- 8.3.2 The Case n=2 -- 8.3.3 A Special Family of Polygons -- 8.3.4 Cutting-Gluing Operations -- 8.3.5 Signature Calculation -- References -- 9 Equilateral Convex Triangulations of R P2 with Three Conical Points of Equal Defect -- 9.1 Introduction -- 9.2 Triangulations of R P2 with Three Marked Points with Defects 2π/3 -- 9.3 Moduli Space of Flat Metrics on S2 with Six Pair-Wise Centrally Symmetric Conical Points of Equal Defect -- 9.4 A Parametrization of Equilateral Triangulations of S2 with Six Centrally-Symmetric Points with Defects 2π/3 -- 9.5 Examples and Computer Computations -- References -- 10 Combination Theorems in Groups, Geometry and Dynamics -- 10.1 Introduction -- 10.2 Klein-Maskit Combination for Kleinian Groups -- 10.3 Simultaneous Uniformization and Quasi-Fuchsian Groups -- 10.3.1 Topologies on Space of Representations -- 10.3.2 Simultaneous Uniformization -- 10.3.3 Geodesic Laminations -- 10.4 Thurston's Combination Theorem for Haken Manifolds.
10.4.1 Non-fibered Haken 3-Manifolds -- 10.4.2 The Double Limit Theorem -- 10.5 Combination Theorems in Geometric Group Theory:Hyperbolic Groups -- 10.5.1 Trees of Spaces -- 10.5.2 Metric Bundles -- 10.5.2.1 Ladders -- 10.5.2.2 Idea Behind the Proof of Theorem 10.18 -- 10.5.3 Relatively Hyperbolic Combination Theorems -- 10.5.3.1 Relatively Hyperbolic Combination Theorem Using Acylindricity -- 10.5.3.2 Relatively Hyperbolic Combination Theorem Using Flaring -- 10.5.4 Effective Quasiconvexity and Flaring -- 10.6 Combination Theorems in Geometric Group Theory:Cubulations -- 10.7 Holomorphic Dynamics and Polynomial Mating -- 10.7.1 Historical Comments -- 10.7.2 Mating of Polynomials -- 10.8 Combining Rational Maps and Kleinian Groups -- 10.8.1 Mating Anti-polynomials with Reflection Groups -- 10.8.1.1 Schwarz Reflection Maps and Motivating Examples -- 10.8.1.2 Necklace Reflection Groups -- 10.8.1.3 Conformal Mating of Anti-polynomials and Necklace Groups -- 10.8.1.4 Examples of the Mating Phenomenon -- 10.8.1.5 The General Theorem -- 10.8.2 Mating Polynomials with Kleinian Groups -- 10.8.2.1 The Fuchsian Case -- 10.8.2.2 The Case of Bers Boundary Groups -- References -- 11 On the Pullback Relation on Curves Induced by a Thurston Map -- 11.1 Introduction -- 11.2 Conventions and Notation -- 11.3 Non-dynamical Properties of f -- 11.3.1 Known General Results -- 11.3.2 Mechanisms for Triviality of f -- 11.3.3 Computation of f -- 11.3.4 When Each Curve Has a Nontrivial Preimage -- 11.4 Dynamical Properties -- 11.4.1 General Properties -- 11.4.2 Bounds on the Size of the Attractor -- 11.4.3 Examples with Symmetries -- 11.4.4 Maps with the Same Fundamental Invariants -- 11.4.5 Expanding vs. Nonexpanding Maps -- References -- 12 The Pullback Map on Teichmüller Space Induced from a Thurston Map -- 12.1 Thurston's Characterization Theorem -- 12.1.1 Levy Cycles.
12.1.2 An Application to Matings.
Record Nr. UNISA-996485660603316
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
In the tradition of Thurston II : geometry and groups / / Ken'ichi Ohshika, Athanase Papadopoulos, editors
In the tradition of Thurston II : geometry and groups / / Ken'ichi Ohshika, Athanase Papadopoulos, editors
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (525 pages)
Disciplina 516
Soggetto topico Geometry
Group theory
Geometria
Teoria de grups
Soggetto genere / forma Llibres electrònics
ISBN 3-030-97560-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 2 A Survey of Complex Hyperbolic Kleinian Groups -- 2.1 Introduction -- 2.2 Complex Hyperbolic Space -- 2.3 Basics of Discrete Subgroups of PU(n,1) -- 2.4 Margulis Lemma and Thick-Thin Decomposition -- 2.5 Geometrically Finite Groups -- 2.6 Ends of Negatively Curved Manifolds -- 2.7 Critical Exponent -- 2.8 Examples -- 2.9 Complex Hyperbolic Kleinian Groups and Function Theory on Complex Hyperbolic Manifolds -- 2.10 Conjectures and Questions -- Appendix A: Horofunction Compactification -- Appendix B: Two Classical Peano Continua -- Appendix C: Gromov-Hyperbolic Spaces and Groups -- Appendix D: Orbifolds -- Appendix E: Ends of Spaces -- Appendix F: Generalities on Function Theory on Complex Manifolds -- Appendix G (by Mohan Ramachandran): Proof of Theorem 2.19 -- References -- 3 Möbius Structures, Hyperbolic Ends and k-Surfaces in Hyperbolic Space -- 3.1 Overview -- 3.1.1 Hyperbolic Ends and Möbius Structures -- 3.1.2 Infinitesimal Strict Convexity, Quasicompleteness and the Asymptotic Plateau Problem -- 3.1.3 Schwarzian Derivatives -- 3.1.4 Closing Remarks and Acknowledgements -- 3.2 Möbius Structures -- 3.2.1 Möbius Structures -- 3.2.2 The Möbius Disk Decomposition and the Join Relation -- 3.2.3 Geodesic Arcs and Convexity -- 3.2.4 The Kulkarni-Pinkall Form -- 3.2.5 Analytic Properties of the Kulkarni-Pinkall Form -- 3.3 Hyperbolic Ends -- 3.3.1 Hyperbolic Ends -- 3.3.2 The Half-Space Decomposition -- 3.3.3 Geodesic Arcs and Convexity -- 3.3.4 Ideal Boundaries -- 3.3.5 Extensions of Möbius Surfaces -- 3.3.6 Left Inverses and Applications -- 3.4 Infinitesimally Strictly Convex Immersions -- 3.4.1 Infinitesimally Strictly Convex Immersions -- 3.4.2 A Priori Estimates -- 3.4.3 Cheeger-Gromov Convergence -- 3.4.4 Labourie's Theorems and Their Applications -- 3.4.5 Uniqueness and Existence.
Appendix A: A Non-complete k-Surface -- Appendix B: Category Theory -- References -- 4 Cone 3-Manifolds -- 4.1 Introduction -- 4.2 Cone Manifolds -- 4.3 Hyperbolic Dehn Filling -- 4.4 Local Rigidity -- 4.5 Sequences of Cone Manifolds -- 4.5.1 Compactness Theorem -- 4.5.2 Cone-Thin Part -- 4.5.3 Decreasing Cone Angles: Global Rigidity -- 4.5.4 Increasing Cone Angles -- 4.6 Examples -- 4.6.1 Hyperbolic Two-Bridge Knots and Links -- 4.6.2 Montesinos Links -- 4.6.3 A Cusp Opening -- 4.6.4 Borromean Rings -- 4.6.5 Borromean Rings Revisited: Spherical Structures -- References -- 5 A Survey of the Thurston Norm -- 5.1 Introduction -- Organization -- Conventions and Notation -- 5.2 Foundations of the Thurston Norm -- 5.2.1 Thurston Norm -- 5.2.2 Norm Balls and Fibrations Over a Circle -- 5.2.3 Norm-Minimizing Surfaces and Codimension-1 Foliations -- 5.2.4 Singular and Gromov Norms -- 5.3 Alexander and Teichmüller Polynomials -- 5.3.1 Alexander Polynomial -- 5.3.2 Abelian Torsion -- 5.3.3 Teichmüller Polynomial -- 5.4 Seiberg-Witten Invariant -- 5.4.1 Seiberg-Witten Theory -- 5.4.2 Seiberg-Witten Invariant of a 3-Manifold -- 5.4.3 Complexity of Surfaces in a 4-Manifold -- 5.4.4 Harmonic Norm -- 5.5 Floer Homology -- 5.5.1 Heegaard Floer Homology -- 5.5.2 Knot Floer Homology -- 5.6 Torsion Invariants -- 5.6.1 Reidemeister Torsion -- 5.6.2 Twisted Alexander Polynomials -- 5.6.3 Higher-Order Alexander Polynomials -- 5.6.4 L2-Alexander Torsion -- 5.7 Triangulations -- 5.7.1 Thurston Norm Via Normal Surfaces -- 5.7.2 Z / 2 Z-Thurston Norm and Complexity of 3-Manifolds -- 5.8 Profinite Rigidity -- 5.9 Conjectures and Questions -- 5.9.1 Realization Problem -- 5.9.2 Complexity Functions for Circle Bundles -- 5.9.3 Twisted Alexander Polynomials for Hyperbolic Knots -- 5.9.4 Higher-Order Alexander Polynomials and the Knot Genus.
5.9.5 Lower Bounds on Complexity of 3-Manifolds -- 5.9.6 Thurston Norm Balls of Finite Covers -- References -- 6 From Hyperbolic Dehn Filling to Surgeries inRepresentation Varieties -- 6.1 Introduction -- 6.2 Hyperbolic Dehn Surgery -- 6.2.1 Dehn Surgery -- 6.2.2 Hyperbolic Dehn Surgery -- 6.2.3 Haken Manifolds and Thurston's Uniformization -- 6.3 Deformations of Hyperbolic Structures by Bending -- 6.4 Higher Teichmüller Theory -- 6.4.1 The Teichmüller Space -- 6.4.2 Higher Teichmüller Spaces -- 6.4.3 -Positive Representations -- 6.5 Non-abelian Hodge Theory -- 6.5.1 Moduli Spaces of G-Higgs Bundles -- 6.5.2 G-Hitchin Equations -- 6.5.3 The Non-abelian Hodge Correspondence -- 6.6 Surgeries in Representation Varieties-General Theory -- 6.6.1 Topological Gluing Construction -- 6.6.2 Gluing in Exceptional Components of the Moduli Space -- 6.6.2.1 Parabolic GL( n,C )-Higgs Bundles -- 6.6.3 Complex Connected Sum of Riemann Surfaces -- 6.6.4 Gluing at the Level of Solutions to Hitchin's Equations -- 6.6.4.1 The Local Model -- 6.6.4.2 Approximate Solutions of the SL(2,R)-Hitchin Equations -- 6.6.5 Approximate Solutions to the G-Hitchin Equations -- 6.6.6 The Contraction Mapping Argument -- 6.6.7 Correcting an Approximate Solution to an Exact Solution -- 6.6.8 Topological Invariants -- 6.7 Examples: Model Higgs Bundles in Exceptional Components of Orthogonal Groups -- 6.7.1 SO( p,q )-Higgs Bundle Data -- 6.7.2 Hitchin Equations for Orthogonal Groups -- 6.7.3 Model Parabolic SL( 2,R )-Higgs Bundles -- 6.7.4 Parabolic SO( p,p+1 )-Models -- 6.7.4.1 Models via the Irreducible Representation SL( 2,R )-3muSO( p,p+1 ) -- 6.7.4.2 Models via the General Map -- 6.7.5 Gauge-Theoretic Gluing of Parabolic SO( p,p+1 )-Higgs Bundles -- 6.7.6 Model Representations in the Exceptional Components of R( SO( p,p+1 ) ) -- 6.7.7 Model Representations and Positivity -- References.
7 Acute Geodesic Triangulations of Manifolds -- 7.1 Introduction -- 7.2 In Dimension Three and Higher -- 7.2.1 Polytopes and Dehn-Sommerville Equations -- 7.2.2 Spherical Complexes -- 7.2.3 Dimension Four and Five -- 7.2.4 R3, S3 and More -- 7.3 Dimension Two: General Riemannian and Flat Cone Metrics -- 7.3.1 Riemannian Surfaces -- 7.3.2 Euclidean and Flat Cone Surfaces -- 7.3.3 Parametrizing Equilateral Triangulations -- 7.3.4 Aperiodic Tilings -- 7.4 Round Spheres -- 7.4.1 Acute Triangulations from Right-Angled Hyperbolic 3-Polytopes -- 7.4.2 The Koebe-Andreev-Thurston Theorem and Its Generalizations -- 7.4.3 CAT(κ) Spaces -- References -- 8 Signature Calculation of the Area Hermitian Form on Some Spaces of Polygons -- 8.1 Introduction -- 8.2 Basic Facts on Hermitian Forms -- 8.3 Spaces of Polygons and Signature Calculation -- 8.3.1 The Area Hermitian Form and the Formula for Its Signature -- 8.3.2 The Case n=2 -- 8.3.3 A Special Family of Polygons -- 8.3.4 Cutting-Gluing Operations -- 8.3.5 Signature Calculation -- References -- 9 Equilateral Convex Triangulations of R P2 with Three Conical Points of Equal Defect -- 9.1 Introduction -- 9.2 Triangulations of R P2 with Three Marked Points with Defects 2π/3 -- 9.3 Moduli Space of Flat Metrics on S2 with Six Pair-Wise Centrally Symmetric Conical Points of Equal Defect -- 9.4 A Parametrization of Equilateral Triangulations of S2 with Six Centrally-Symmetric Points with Defects 2π/3 -- 9.5 Examples and Computer Computations -- References -- 10 Combination Theorems in Groups, Geometry and Dynamics -- 10.1 Introduction -- 10.2 Klein-Maskit Combination for Kleinian Groups -- 10.3 Simultaneous Uniformization and Quasi-Fuchsian Groups -- 10.3.1 Topologies on Space of Representations -- 10.3.2 Simultaneous Uniformization -- 10.3.3 Geodesic Laminations -- 10.4 Thurston's Combination Theorem for Haken Manifolds.
10.4.1 Non-fibered Haken 3-Manifolds -- 10.4.2 The Double Limit Theorem -- 10.5 Combination Theorems in Geometric Group Theory:Hyperbolic Groups -- 10.5.1 Trees of Spaces -- 10.5.2 Metric Bundles -- 10.5.2.1 Ladders -- 10.5.2.2 Idea Behind the Proof of Theorem 10.18 -- 10.5.3 Relatively Hyperbolic Combination Theorems -- 10.5.3.1 Relatively Hyperbolic Combination Theorem Using Acylindricity -- 10.5.3.2 Relatively Hyperbolic Combination Theorem Using Flaring -- 10.5.4 Effective Quasiconvexity and Flaring -- 10.6 Combination Theorems in Geometric Group Theory:Cubulations -- 10.7 Holomorphic Dynamics and Polynomial Mating -- 10.7.1 Historical Comments -- 10.7.2 Mating of Polynomials -- 10.8 Combining Rational Maps and Kleinian Groups -- 10.8.1 Mating Anti-polynomials with Reflection Groups -- 10.8.1.1 Schwarz Reflection Maps and Motivating Examples -- 10.8.1.2 Necklace Reflection Groups -- 10.8.1.3 Conformal Mating of Anti-polynomials and Necklace Groups -- 10.8.1.4 Examples of the Mating Phenomenon -- 10.8.1.5 The General Theorem -- 10.8.2 Mating Polynomials with Kleinian Groups -- 10.8.2.1 The Fuchsian Case -- 10.8.2.2 The Case of Bers Boundary Groups -- References -- 11 On the Pullback Relation on Curves Induced by a Thurston Map -- 11.1 Introduction -- 11.2 Conventions and Notation -- 11.3 Non-dynamical Properties of f -- 11.3.1 Known General Results -- 11.3.2 Mechanisms for Triviality of f -- 11.3.3 Computation of f -- 11.3.4 When Each Curve Has a Nontrivial Preimage -- 11.4 Dynamical Properties -- 11.4.1 General Properties -- 11.4.2 Bounds on the Size of the Attractor -- 11.4.3 Examples with Symmetries -- 11.4.4 Maps with the Same Fundamental Invariants -- 11.4.5 Expanding vs. Nonexpanding Maps -- References -- 12 The Pullback Map on Teichmüller Space Induced from a Thurston Map -- 12.1 Thurston's Characterization Theorem -- 12.1.1 Levy Cycles.
12.1.2 An Application to Matings.
Record Nr. UNINA-9910586595703321
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui