A 4-dimensional light bulb theorem for disks
arXiv:2109.13397
Abstract
We give a 4-dimensional light bulb theorem for properly embedded disks, generalizing recent work of Gabai and Kosanovic-Teichner in certain contexts, and extending the 4-dimensional light bulb theorem for 2-spheres due to Gabai and Schneiderman-Teichner. In particular, we provide conditions under which homotopic disks properly embedded in a compact 4-manifold X with a common dual in the interior of X are smoothly isotopic rel boundary. We also provide a new geometric interpretation of the Dax invariant, to aid in its computation.
Updated version -- the hypotheses and conclusion of the main result have been made more general, Figure 14 and Remarks 4.2 and 4.3 added, and additional small revisions/corrections throughout. Comments encouraged!