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Central extensions of word hyperbolic groups. (English) Zbl 0871.20032
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 The fact that these groups are automatic is an (unpublished) result due to Thurston.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.

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
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