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arXiv · 2603.22202

Non-smoothable surfaces in the 4-sphere

Anthony Conway·Daniel Galvin
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Abstract

We construct examples of non-smoothable surfaces in the $4$-sphere, thereby answering Question 4.32 on the K3 problem list. These surfaces are non-orientable and have knot group of order $2$, thus simultaneously answering Question 4.29(a) on the K3 problem list.

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Anthony Conway, Daniel Galvin. 2026-05-21. Non-smoothable surfaces in the 4-sphere. https://arxiv.org/abs/2603.22202

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