scl

This book is an introduction to the theory of stable commutator length and the related subjects of quasimorphisms and bounded cohomology.

The book was published by the Mathematical Society of Japan in June 2009 as volume 20 in their MSJ Memoirs series. The .pdf is available for download here with their permission, although I encourage you to buy a physical copy if you find this version useful.

Download .pdf

Associated software (including scallop) can be downloaded from Alden Walker's GitHub page.

Zentralblatt MATH review by Athanase Papadopoulos

MathSciNet review by Athanase Papadopoulos

TABLE OF CONTENTS

---

• Preface
• Acknowledgements
• Chapter 1: Surfaces
  • Triangulating surfaces
  • Hyperbolic surfaces
• Chapter 2: Stable commutator length
  • Commutator length and stable commutator length
  • Quasimorphisms
  • Examples
  • Bounded cohomology
  • Bavard's Duality Theorem
  • Stable commutator length as a norm
  • Extremal quasimorphisms
  • Further properties
• Chapter 3: Hyperbolicity and spectral gaps
  • Hyperbolic manifolds
  • Spectral Gap Theorem
  • Examples
  • Hyperbolic groups
  • Counting quasimorphisms
  • Mapping class groups
  • Out(F_n)
• Chapter 4: Free and surface groups
  • The Rationality Theorem
  • Geodesics on surfaces
  • Small cancellation theory
• Chapter 5: Irrationality and dynamics
  • Stein-Thompson groups
  • Groups with few quasimorphisms
  • Braid groups and transformation groups
• Chapter 6: Combable functions and ergodic theory
  • An example
  • Groups and automata
  • Combable functions
  • Counting quasimorphisms
  • Patterson-Sullivan measures
• Bibliography