Smale: the generalized Poincaré conjecture above dimension four

What changed

The generalized Poincaré problem was solved in smooth dimensions five and higher.

Scientific scope

1961 high-dimensional result only; dimensions three and four and later h-cobordism developments separate.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact 1961 Annals of Mathematics paper. The classical three-dimensional conjecture, dimension four, the h-cobordism theorem’s broader development and Perelman’s later work remain separate.

Contributors

• Stephen Smale · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Smale, Generalized Poincaré Conjecture in Dimensions Greater Than Four
• MathNet record for Smale generalized Poincaré paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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