Description
Book SynopsisThe study of the mapping class group Mod(S) is a classical topic that experiences a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem.
Trade Review"It is clear that a lot of care has been taken in the production of this book, something that indicates the authors' love for the subject. This book should now become the standard text for the subject."--Stephen P Humphries, Mathematical Reviews "[T]his is a very pleasant and appealing book and it is an excellent reference for any reader willing to learn about this fascinating part of mathematics."--Raquel Diaz, Alvaro Martinez, European Mathematical Society
Table of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*Acknowledgments, pg. xiii*Overview, pg. 1*Chapter One. Curves, Surfaces, and Hyperbolic Geometry, pg. 17*Chapter Two. Mapping Class Group Basics, pg. 44*Chapter Three. Dehn Twists, pg. 64*Chapter Four. Generating The Mapping Class Group, pg. 89*Chapter Five. Presentations And Low-Dimensional Homology, pg. 116*Chapter Six. The Symplectic Representation and the Torelli Group, pg. 162*Chapter Seven. Torsion, pg. 200*Chapter Eight. The Dehn-Nielsen-Baer Theorem, pg. 219*Chapter Nine. Braid Groups, pg. 239*Chapter Ten. Teichmuller Space, pg. 263*Chapter Eleven. Teichmuller Geometry, pg. 294*Chapter Twelve. Moduli Space, pg. 342*Chapter Thirteen. The Nielsen-Thurston Classification, pg. 367*Chapter Fourteen. Pseudo-Anosov Theory, pg. 390*Chapter Fifteen. Thurston'S Proof, pg. 424*Bibliography, pg. 447*Index, pg. 465
