feat: add generalized topological Poincaré in dim ≥ 5 (Smale) eval problem#296
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…le) eval problem This PR adds Smale's generalized topological Poincaré conjecture in dimensions n ≥ 5 as a new eval problem: every Hausdorff n-manifold homotopy-equivalent to 𝕊ⁿ is homeomorphic to 𝕊ⁿ. Specialization to n ≥ 5 of mathlib's generalized `proof_wanted`. Smale 1961 (Fields Medal 1966) for smooth M via the h-cobordism theorem; topological version completed by Newman 1966 and Connell 1967. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the generalized topological Poincaré conjecture in dimensions ≥ 5 as a new lean-eval challenge problem: for
n ≥ 5, every Hausdorffn-manifold homotopy-equivalent to𝕊ⁿis homeomorphic to𝕊ⁿ.Specialization to
n ≥ 5of mathlib's generalizedproof_wanted ContinuousMap.HomotopyEquiv.nonempty_homeomorph_sphereinMathlib/Geometry/Manifold/PoincareConjecture.lean. Stephen Smale 1961 (Ann. of Math. 74), originally for smoothMvia the h-cobordism theorem (Smale's main contribution); the topological version (no smoothness assumption) was completed by Newman in 1966 and Connell in 1967. Smale received the Fields Medal in 1966.mathlib has homotopy equivalences (
≃ₕ), homeomorphisms (≃ₜ),ChartedSpace, and the unit sphere as a topological space — but no h-cobordism theorem, no handle decompositions, and no Poincaré conjecture in any dimension.Companion problems: #293 (3D topological, Perelman), #294 (3D smooth, Perelman), #295 (4D topological, Freedman).
🤖 Prepared with Claude Code