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From Knots to Four-Manifolds
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1 cited passage ↓1 problem ↓Record icm-2026-doi-25M1806703 ↓
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The survey states the smooth four-dimensional Poincaré conjecture as an open question, distinct from Freedman’s topological four-dimensional result.
Passage ID: poincare-conjecture:entry:smooth-four:v1
Source item: §3, Conjecture 3.1 and preceding topological classification
Source record: manolescu-four-manifolds@icm-2026-doi-25M1806703
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v13
Source assessment
Proved
Established result in cited source
Freedman’s topological conclusion does not identify a smooth structure or imply the smooth four-dimensional conjecture.
Observed Oct 12, 2026
Scope
The topological four-dimensional theorem
Source assessment
Open
Open question in cited source
This is a separate conjecture in dimension four; simple connectivity alone is insufficient for its hypothesis.
Observed Oct 12, 2026
Scope
The smooth four-dimensional Poincaré question
Connection
Homeomorphism and diffeomorphism are different requirements in dimension four.
Connection
The four-dimensional smooth question concerns a different dimension and equivalence notion.
Question
Poincaré conjecture
Recorded authorship
Ciprian Manolescu
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From Knots to Four-Manifolds
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