On bounded cohomology of amalgamated products of groups. (Q1777672)

In this interesting paper the author investigates the structure of the singular part of the second bounded cohomology group, \(H^2 _{b,2}(G)\), with coefficients in the additive group of reals \(\mathbb{R}\) with trivial action, when \(G\) is an amalgamated product of groups. \(H^2_{b,2}(G)\cong PX(G)/X(G)\), as vector spaces, where \(X(G)\) is the space of additive characters \(G\to\mathbb{R}\) and \(PX(G)\) is the space of pseudocharacters. In certain cases, the author constructs an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.