Mathematical Society of Japan Memoirs


Danny Calegari

Book information

Danny Calegari

Publication information
MSJ Memoirs, Volume 20
Tokyo, Japan: The Mathematical Society of Japan, 2009
209 pp.

Publication date: 2009
First available in Project Euclid: 24 November 2014

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Zentralblatt MATH:

Mathematical Reviews (MathSciNet):

Primary: 20J05: Homological methods in group theory 57M07: Topological methods in group theory
Secondary: 20F12: Commutator calculus 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups 37E45: Rotation numbers and vectors 37J05: General theory, relations with symplectic geometry and topology 90C05: Linear programming

stable commutator length bounded cohomology rationality Bavard's Duality Theorem hyperbolic groups free groups Thurston norm Bavard's Conjecture rigidity immersions causality group dynamics Markov chains central limit theorem combable groups finite state automata

Copyright © 2009, The Mathematical Society of Japan

Danny Calegari, scl (Tokyo: The Mathematical Society of Japan, 2009)

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This book is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology, and many other subjects. We use constructive methods whenever possible, and focus on fundamental and explicit examples. We give a self-contained presentation of several foundational results in the theory, including Bavard’s Duality Theorem, the Spectral Gap Theorem, the Rationality Theorem, and the Central Limit Theorem. The contents should be accessible to any mathematician interested in these subjects, and are presented with a minimal number of prerequisites, but with a view to applications in many areas of mathematics.