Abstract
We investigate constraints on embeddings of a nonorientable surface in a 4-manifold with the homology of M x I, where M is a rational homology 3-sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface, and either the Ozsvath-Szabo d-invariants or Atiyah-Singer rho-invariants of M. One consequence is that the minimal genus of a smoothly embedded surface in L(2k, q) x I is the same as the minimal genus of a surface in L(2k, q). We also consider embeddings of nonorientable surfaces in closed 4-manifolds.