  Autostackability for finitely generated groups is defined via a topological
property of the associated Cayley graph which can be encoded in a finite state
automaton. Autostackable groups have solvable word problem and an effective
inductive procedure for constructing van Kampen diagrams with respect to a
canonical finite presentation. A comparison with automatic groups is given.
Another characterization of autostackability is given in terms of
prefix-rewriting systems. Every group which admits a finite complete rewriting
system or an asynchronously automatic structure with respect to a prefix-closed
set of normal forms is also autostackable. As a consequence, the fundamental
group of every closed 3-manifold with any of the eight possible uniform
geometries is autostackable.
