Neumann, Walter D.; Reeves, Lawrence Central extensions of word hyperbolic groups. (English) Zbl 0871.20032 Ann. Math. (2) 145, No. 1, 183-192 (1997). The authors prove that central extensions of word hyperbolic groups by finitely generated abelian groups are biautomatic. The fact that these groups are automatic is an (unpublished) result due to Thurston. The authors prove also that every 2-dimensional cohomology class on a word hyperbolic group can be represented by a bounded cocycle. In the last section of the paper, the authors discuss the relations between various concepts of “weak boundedness” of a 2-cocycle on an arbitrary finitely generated group. These concepts are related to quasi-isometry properties of central extensions. They show that for cohomology classes, the various notions of weak boundedness are equivalent, but it is unknown whether a weakly bounded cohomology class must be bounded. Reviewer: A.Papadopoulos (Strasbourg) Cited in 2 ReviewsCited in 12 Documents MSC: 20F65 Geometric group theory 20F05 Generators, relations, and presentations of groups 20E22 Extensions, wreath products, and other compositions of groups 57M07 Topological methods in group theory Keywords:central extensions; word hyperbolic groups; biautomatic groups; bounded cocycles; finitely generated groups; weakly bounded cohomology classes; quasi-isometries PDFBibTeX XMLCite \textit{W. D. Neumann} and \textit{L. Reeves}, Ann. Math. (2) 145, No. 1, 183--192 (1997; Zbl 0871.20032) Full Text: DOI arXiv