  Thurston has claimed (unpublished) that central extensions of word hyperbolic
groups by finitely generated abelian groups are automatic. We show that they
are in fact biautomatic. Further, we show that every 2-dimensional cohomology
class on a word hyperbolic group can be represented by a bounded 2-cocycle.
This lends weight to the claim of Gromov that for a word hyperbolic group, the
cohomology in every dimension is bounded.
