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Calegari, Danny (2009) Scl. Mathematical Society of Japan Memoirs. No.20. Mathematical Society of Japan , Tokyo. ISBN 978-4-931469-53-2. http://resolver.caltech.edu/CaltechAUTHORS:20180808-090434034

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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.


Item Type:Book
Related URLs:
URLURL TypeDescription
https://doi.org/10.2969/msjmemoirs/020010000DOIBook
Alternate Title:Stable Commutator Length
Additional Information:© 2009 The Mathematical Society of Japan.
Subject 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
Classification Code:MSC: Primary: 20J05: Homological methods in group theory 57M07: Topological methods in group theory
Record Number:CaltechAUTHORS:20180808-090434034
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180808-090434034
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88647
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Aug 2018 16:14
Last Modified:08 Aug 2018 16:14

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