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