A note on three-fold branched covers of $S^4$

Ryan Blair; Patricia Cahn; Alexandra Kjuchukova; Jeffrey Meier

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arXiv · 1909.11788

A note on three-fold branched covers of $S^4$

Ryan Blair·Patricia Cahn·Alexandra Kjuchukova·Jeffrey Meier

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Abstract

We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^4$, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property.

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Ryan Blair, Patricia Cahn, Alexandra Kjuchukova, Jeffrey Meier. 2019-09-25. A note on three-fold branched covers of $S^4$. https://arxiv.org/abs/1909.11788

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