scl



This book is an introduction to the theory of stable commutator length, especially in the context of groups of (coarse) negative curvature. This is an important subtopic in the theory of bounded cohomology, and has connections with dynamics, geometric group theory, symplectic topology, and many other subjects. The book presents (in a largely self-contained way) several foundational results in the theory, including Bavard's duality theorem, the spectral gap theorem, the rationality theorem and the central limit theorem. The importance of word-hyperbolic groups, and especially fundamental groups of hyperbolic 2- and 3-manifolds, is emphasized throughout.

Sadayoshi Kojima has kindly solicited this book for publication, and it will ultimately appear as a volume in the MSJ Memoirs series, published by the Mathematical Society of Japan. I expect to continue to make the text of the book freely available after publication.

I have decided to make preliminary versions of this book available, for several reasons. Firstly, in order to get feedback/corrections/etc. Secondly, because the book is modular and therefore even though several sections are not yet finished, some parts are in good enough shape to serve as a useful reference. Thirdly, I hope that sticking my neck out like this will give me an incentive to keep writing. The (preliminary) draft of the book is available here. If you download this book, please let me know what you think, if you think something should be changed/added etc.


Version: last updated 8th May 2008. Thanks to Koji Fujiwara, Justin Malestein, Jason Manning, Geoff Mess, Andy Putman and Dongping Zhuang for additions and corrections.


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