Regular combings, nonpositive curvature and the quasiconvexity of abelian subgroups

We study the geometry of abelian subgroups relative to combings (normal forms) of automatic groups and groups which act properly and cocompactly on spaces of nonpositive curvature. We prove that in general combings which arise in the latter context are incompatible (in a sense which we make precise) with regular combings, the fundamental objects of automatic group theory. © 1993.