A classification of 2-complexes with nontrivial self-covers

The main result is the classification of finite regular 2-complexes which have a nontrivial finite-sheeted self-cover. It is shown that a 2-complex K is a member of this class if and only if it may be decomposed as a collection of annuli and circles in the sense made precise in the paper. Intuitively, K is recovered by gluing the boundary components of the annuli to the circles via covering maps.