Bounded cohomology of group constructions

It is proved that the singular partH _b ^2/(2) (G) of the second group of bounded homology of the discrete groupG is isomorphic to the space of 2-cocycles that vanish on the diagonal. For groupsG representable as HNN-extensions or free products with amalgamation, as well as for groupsG with one defining relation, conditions for the infinite-dimensionality ofH _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. Translated fromMatematicheskie Zametki, Vol. 59, No. 4, pp. 546–550, April, 1996. This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00239.