A Concordance Analogue of the 4D Light Bulb Theorem

We prove a concordance analogue of Gabai's 4D light bulb theorem. That is, we show that when R and R' are homotopic, embedded 2-spheres in a 4-manifold X-4, where pi(1)(X-4) has no 2-torsion and one of R or R' has a transverse sphere, then R and R' are concordant. When pi(1)(X-4) has 2-torsion, we give a similar statement with extra hypotheses as in the 4D light bulb theorem. We also give similar statements when R and R' are orientable positive-genus surfaces.