feat: add 4D topological Poincaré conjecture (Freedman) eval problem#295
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feat: add 4D topological Poincaré conjecture (Freedman) eval problem#295kim-em wants to merge 1 commit into
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This PR adds the 4D topological Poincaré conjecture (Freedman 1982) as a new eval problem: every Hausdorff 4-manifold homotopy-equivalent to 𝕊⁴ is homeomorphic to 𝕊⁴. Specialization to n = 4 of mathlib's generalized `proof_wanted ContinuousMap.HomotopyEquiv.nonempty_homeomorph_sphere`. Fields Medal 1986; proof uses Casson handles and the Bing-topology infinite-process construction. The corresponding smooth 4D Poincaré conjecture remains famously open and is not included. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the 4D topological Poincaré conjecture as a new lean-eval challenge problem: every Hausdorff 4-manifold homotopy-equivalent to
𝕊⁴is homeomorphic to𝕊⁴.Specialization to
n = 4of mathlib's generalizedproof_wanted ContinuousMap.HomotopyEquiv.nonempty_homeomorph_sphereinMathlib/Geometry/Manifold/PoincareConjecture.lean. Michael Freedman's 1982 theorem (J. Differential Geom. 17), Fields Medal 1986. The proof uses Casson handles and the Bing-topology infinite-process construction.The corresponding smooth 4D Poincaré conjecture remains famously open and is not included as an eval problem.
mathlib has homotopy equivalences (
≃ₕ), homeomorphisms (≃ₜ),ChartedSpace, and the unit sphere as a topological space — but no Casson handles, no Freedman's theorem.🤖 Prepared with Claude Code