Bounded cohomology of group constructions

It is proved that the singular part $H_b^{2/(2)}(G)$ of the second group of bounded homology of the discrete group $G$ is isomorphic to the space of 2-cocycles that vanish on the diagonal. For groups $G$ representable as HNN-extensions or free products with amalgamation, as well as for groups $G$ with one defining relation, conditions for the infinite-dimensionality of $H_b^{2/(2)}(G)$ are found. Some applications of bounded cohomology to the width problem for verbal subgroups and to the boundedness problem for group presentations are indicated.