Theory of bounded groups and their bounded cohomology
Bounded cohomology H can be defined for groups and for topological spaces. Recent work has shown that \(H^ *_ b(M)\) of a topological space M depends only on \(\pi _ 1(M)\). In this paper we consider a new concept - a bounded group - and thereby expand the definition of bounded cohomology. We prove that bounded cohomology groups are themselves bounded groups and develop their properties in lower dimensions. In particular, elements of \(H^ 2_ b(G,A)\) classify bounded group extensions of G by A. As an application of the theory of bounded groups we construct the Lyndon spectral sequence and obtain a result relating the bounded cohomology of a group and its subgroup.
scientific article; zbMATH DE number 3998762