Mathematical Society of Japan Memoirs

scl

Danny Calegari

Book information

Author
Danny Calegari

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

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

Permanent link to this book
https://projecteuclid.org/euclid.msjm/1416864672

Digital Object Identifier:
doi:10.2969/msjmemoirs/020010000

ISBN:
978-4-931469-53-2

Zentralblatt MATH:
1187.20035

Mathematical Reviews (MathSciNet):
MR2527432

Subjects
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

Keywords
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

Rights
Copyright © 2009, The Mathematical Society of Japan

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

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Abstract

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.