Thurston's work on surfaces / Albert Fathi, François Laudenbach, and Valentin Poénaru ; translated by Djun Kim and Dan Margalit.

Format:

Book

Author/Creator:

Fathi, Albert, author.

Laudenbach, François, author.

Poenaru, Valentin, author.

Contributor:

Kim, Djun M., translator.

Margalit, Dan, 1976- translator.

Series:

Mathematical notes (Princeton University Press) ; 48.

Mathematical notes (Princeton University Press) ; 48

Standardized Title:

Travaux de Thurston sur les surfaces. English.

Language:

English

Subjects (All):

Homeomorphisms.

Surfaces.

Dynamics.

Physical Description:

1 online resource (274 pages)

Place of Publication:

Princeton, New Jersey ; Oxford : Princeton University Press, 2012.

Summary:

This book provides a detailed exposition of William Thurston's work on surface homeomorphisms, available here for the first time in English. Based on material of Thurston presented at a seminar in Orsay from 1976 to 1977, it covers topics such as the space of measured foliations on a surface, the Thurston compactification of Teichmüller space, the Nielsen-Thurston classification of surface homeomorphisms, and dynamical properties of pseudo-Anosov diffeomorphisms. Thurston never published the complete proofs, so this text is the only resource for many aspects of the theory.Thurston was awarded the prestigious Fields Medal in 1982 as well as many other prizes and honors, and is widely regarded to be one of the major mathematical figures of our time. Today, his important and influential work on surface homeomorphisms is enjoying continued interest in areas ranging from the Poincaré conjecture to topological dynamics and low-dimensional topology.Conveying the extraordinary richness of Thurston's mathematical insight, this elegant and faithful translation from the original French will be an invaluable resource for the next generation of researchers and students.

Contents:

Frontmatter

Contents

Preface

1 An Overview of Thurston’s Theorems on Surfaces

2 Some Reminders about the Theory of Surface Diffeomorphisms

3 Review of Hyperbolic Geometry in Dimension 2

4 The Space of Simple Closed Curves in a Surface

A. Pair of Pants Decompositions of a Surface

Appendix A

5 Measured Foliations

B Spines of Surfaces

Appendix B

6 The Classification of Measured Foliations

C Explicit Formulas for Measured Foliations

Appendix C

7 Teichmuller Space

8 The Thurston Compactification of Teichmuller Space

D Estimates of Hyperbolic Distances

Appendix D

9 The Classification of Surface Diffeomorphisms

10 Some Dynamics of Pseudo-Anosov Diffeomorphisms

11 Thurston’s Theory for Surfaces with Boundary

12 Uniqueness Theorems for Pseudo-Anosov Diffeomorphisms

13 Constructing Pseudo-Anosov Diffeomorphisms

14 Fibrations over S1 with Pseudo-Anosov Monodromy

15 Presentation of the Mapping Class Group

Bibliography

Index

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9781400839032

1400839033

OCLC:

1255223793