Thurston has claimed (unpublished) that central extensions of word hyperbolic groups by finitely generated abelian groups are automatic.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 cohomolog...

We present an explicit construction for the central extension of the group Map(X, G) where X is a compact manifold and G is a Lie group. If X is a complex curve we obtain a simple construction of the extension by the Picard variety Pic(X). The construction is easily adapted to the extension of Aut(E), the gauge group of automorphisms of a nontrivial vector bundle E.

Polynomial-time algorithms are given to find a central decomposition of maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of finite ∗-rings and also the Las Vegas C-MeatAxe. When p is small, the probabilistic methods can be replaced by deterministic polynomial-time algorithms. The me...