# Four-manifolds as three-fold covers of $S^4$

### Abstract

I will prove that every geometrically simply-connected four-manifold arises as a 3-fold irregular cover of $S^4$ branched along an embedded surface. This is a four-dimensional analogue of a classical result of Hilden and relies on adapting his technique to the context of trisections of four-manifolds and embedded surfaces. I’ll review the necessary tools and sketch out the proof.

Joint work with Blair, Cahn, Meier.

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