The smooth four-dimensional Poincaré conjecture

Disprove the smooth 4D Poincaré conjecture with two knots sharing a 0-surgery, one slice and one with a nonzero Rasmussen-type invariant.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"geometry-topology"
5	],
6	"type": "construction",
7	"also": [
8	"proof"
9	],
10	"source": {
11	"key": "frontiermath-open",
12	"name": "FrontierMath: Open Problems",
13	"url": "https://epoch.ai/frontiermath/open-problems/smooth-poincare-4d",
14	"id": "smooth-poincare-4d",
15	"curator": "Epoch AI",
16	"status": "unsolved",
17	"as_of": "2026-10-20",
18	"catalog": "0521c19bbd38"
19	},
20	"review": true,
21	"approval": "first-time"
22	}