A 4-dimensional light bulb theorem for properly embedded disks

A 4-dimensional light bulb theorem for disks

We give two versions of a 4-dimensional light bulb theorem for properly embedded disks.In particular, we provide conditions under which a pair of disks properly embedded in a 4-manifold (with boundary) are smoothly isotopic rel boundary, if these disks(i) are homotopic rel boundary and (ii) share a common dual in the interior of the 4-manifold.We also provide a new geometric interpretation of the dax invariant, to aidin its computation.