Geodesic
Bounded cohomology of group constructions
Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 546-550

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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. 
@article{MZM_1996_59_4_a5,
     author = {R. I. Grigorchuk},
     title = {Bounded cohomology of group constructions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {546--550},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_4_a5/}
}
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R. I. Grigorchuk. Bounded cohomology of group constructions. Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 546-550. http://geodesic.mathdoc.fr/item/MZM_1996_59_4_a5/