Parallel poly-pushdown groups Original Research Article

We define a class of groups based on parallel computations by pushdown automata. This class generalizes automatic groups. It includes the fundamental groups of all 3-manifolds which obey Thurstonʹs geometrization conjecture. It also includes nilpotent groups of arbitrary class and polynomial degree isoperimetric inequality. It is closed under wreath product, and so contains many groups which are not finitely presented.