Bounded cohomology of closed surfaces
Bounded cohomology was introduced by \textit{M. Gromov} in [Publ. Math., Inst. Hautes Étud. Sci. 56, 5-99 (1982; Zbl 0516.53046)]. The author investigates the third bounded cohomology group of a closed, connected surface of genus greater than one and shows how it relates to the geometry of hyperbolic 3-manifolds. One of the results is a version of the Gromov-Thurston-Mostow Rigidity Theorem which applies to a certain class of hyperbolic 3-manifolds with infinite volume. Previous studies of the bounded cohomology of surfaces have concentrated on the second bounded cohomology group, for example, \textit{R. Brooks} and \textit{C. Series} [Topology 23, 29-36 (1984; Zbl 0523.55011)], \textit{J. Barge} and \textit{E. Ghys} [Invent. Math. 92, No. 3, 509-526 (1988; Zbl 0641.55015)], and \textit{Y. Mitsumatsu} [Topology 23, 465-471 (1984; Zbl 0568.55002)].
scientific article; zbMATH DE number 1034155