Table of Contents

Teichmüller Theory Volume 2
Surface Homeomorphisms and Rational Functions

John H. Hubbard
ISBN 9781943863006
262 pages
hardcover, smythe-sewn binding
108 color illustrations

2016, $75

Index (in pdf)
Table of contents (in html)
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See also:
Volume 1: Teichmüller theory
Volume 3: Manifolds that Fiber over the Circle (not yet published)
Volume 4: Hyperbolization of Haken Manifolds (not yet published)

Chapter 8 The classification of homeomorphisms of surfaces

8.1 The classification theorem
8.2 Periodic and reducible homeomorphisms
8.3 Pseudo-Anosov homeomorphisms
8.4 Proof of the classification theorem
8.5 The structure in the reducible case

Chapter 9 Dynamics of polynomials

9.1 Julia sets
9.2 Fixed points
9.3 Green's functions, Böttcher coordinates
9.4 Extending f₀ to S¹
9.5 External rays at rational angles land

Chapter 10 Rational functions

10.1 Introduction
10.1 Thurston mappings
10.2 Thurston maps associated to spiders
10.3 Thurston obstructions for spider maps and Levy cycles
10.4 Julia sets of quadratic polynomials with superattracting cycles
10.5 Parameter spaces for quadratic polynomials
10.6 The Thurston pullback mapping
10.7 The derivative and coderivative of Thurston pullback mapping
10.8 The necessity of the eigenvalue criterion
10.9 Convergence in moduli spaces implies convergence in Teichmüller space
10.10 Asymptotic geometry of Riemann surfaces
10.11 Sufficiency of the eigenvalue criterion

Appendix C1 The Perron-Frobenius theorem
Appendix C2 The Alexander trick
Appendix C3 Homotopy implies isotopy
Appendix C4 The mapping class group and outer automorphisms
Appendix C5 Totally real stretch factors
Appendix C6 Irrationally indifferent fixed points
Appendix C7 Examples of Thurston pullback maps
Appendix C8 Branched maps with nonhyperbolic orbifolds
Appendix C9 The Sullivan dictionary

Bibliography

Index

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