A 4-dimensional light bulb theorem for disks

Hannah Schwartz

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arXiv · 2109.13397

A 4-dimensional light bulb theorem for disks

Hannah Schwartz

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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.

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Hannah Schwartz. 2021-09-27. A 4-dimensional light bulb theorem for disks. https://arxiv.org/abs/2109.13397

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