David Gabai's smooth 4-dimensional "Light Bulb Theorem'' says that in the absence of involutions in the fundamental group of the ambient 4-manifold, homotopy implies isotopy for embedded 2-spheres which have a common geometric dual. In joint work with Peter Teichner we extend his result to orientable 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to the "homotopy implies isotopy'' question. The invariant takes values in an F2-vector space generated by the involutions in the fundamental group. Our methods also give an alternative approach to Gabai's proof using various maneuvers with Whitney disks and a fundamental isotopy between surgeries along dual circles in an orientable surface.

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