Strong surjections from two-complexes with trivial top-cohomology onto nonorientable surfaces

For every nonorientable closed surface , we present a strong surjection f X→, where X is a finite two-dimensional { cw}-complex with trivial second integer cohomology group. This provides an answer, for all nonorientable closed surfaces, to a problem in topological root theory for which we have hitherto known solutions only for the sphere, the torus, the projective plane and the Klein bottle.