Bounded cohomology of closed surfaces
type: Item
instance of: scholarly article
title: Bounded cohomology of closed surfaces
zbMATH Open document ID: 0881.57019
DOI: 10.1016/S0040-9383(97)00003-7
author: Teruhiko Soma
published in: Topology
publication date: 1998-01-04T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 57N65
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 1034155
zbMATH Keywords: bounded cohomology
zbMATH Keywords: surfaces
zbMATH Keywords: hyperbolic 3-manifolds
zbMATH Keywords: Gromov-Thurston-Mostow rigidity theorem
reviewed by: James Hebda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1034155