Quasi-morphisms on Free Groups

2009/11/23 by Pascal Rolli, Rolli, Pascal · 5 citations
Computer Science · Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0911.4234

13 pages, minor corrections

arxiv created 2009/11/24 · arxiv updated 2009/12/08

Abstract

Let F be the free group over a set of two or more generators. R. Brooks constructed an infinite family of quasi-morphisms on F such that an infinite subfamily gives rise to independent classes in the second bounded cohomology of F, which proves that this space is infinite dimensional. We give a simpler proof of this fact using a different type of quasi-morphisms. After computing the Gromov norm of the corresponding bounded classes, we generalize our example to obtain quasi-morphisms on free products, as well as quasi-morphisms into groups without small subgroups, also known as epsilon-representations.

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