Bounded Cohomology of Discrete Groups

Roberto Frigerio, University of Pisa, Italy.

• (Bounded) cohomology of groups(Bounded) cohomology of groups in low degreeAmenability(Bounded) group cohomology via resolutionsBounded cohomology of topological spaces$\ell^1$-homology and dualitySimplicial volumeThe proportionality principleAdditivity of the simplicial volumeGroup actions on the circleThe Euler class of sphere bundlesMilnor-Wood inequalities and maximal representationsThe bounded Euler class in higher dimensions and the Chern conjectureIndexList of symbolsBibliography

The author manages a near perfect equilibrium between necessary technicalities (always well motivated) and geometric intuition, leading the readers from the first simple definition to the most striking applications of the theory in 13 very pleasant chapters. This book can serve as an ideal textbook for a graduate topics course on the subject and become the much-needed standard reference on Gromov's beautiful theory." — Michelle Bucher"The author very well succeeds to present to the reader an overview of all important applications of bounded cohomology." — Thilo Kuessner, Zentralblatt MATH"This book provides a careful, uniform treatment of the main results of bounded cohomology of discrete groups and its applications, also reflecting recent developments. Moreover, important techniques are highlighted...The 'further readings' sections form a valuable collection of references to current research that will be helpful both for students and for researchers." — Clara Löh, Mathematical Reviews