Non-smoothable surfaces in the 4-sphere
Geometric Topology
2026-05-22 v2
Abstract
We construct examples of non-smoothable surfaces in the -sphere, thereby answering Question 4.32 on the K3 problem list. These surfaces are non-orientable and have knot group of order , thus simultaneously answering Question 4.29(a) on the K3 problem list.
Cite
@article{arxiv.2603.22202,
title = {Non-smoothable surfaces in the 4-sphere},
author = {Anthony Conway and Daniel Galvin},
journal= {arXiv preprint arXiv:2603.22202},
year = {2026}
}
Comments
v1: 17 pages. v2: Reorganisation of the introduction. Weakened Theorem 1.2 to account for an oversight in the proof; see the new Proposition 5.4. The advertised main theorem remains unchanged. 22 pages. 2 Figures