# Topology > 18 AI-made results in topology, each explained in plain English with its trust label, Lean status and sources. Canonical: https://closedform.nishachay.tech/science/mathematics/topology/ Last updated: 2026-10-14 18 results in OpenAI Math 2026. 18 AI-made results in topology, from 26 papers in the OpenAI math collection, each explained in plain English. 3 have a formal Lean proof listed; 15 are claimed in a paper and not yet machine-checked. The oldest question here dates back to 1902: [The Hilbert–Smith conjecture in every dimension](https://closedform.nishachay.tech/e/openai-math-2026-304/). Rated Landmark: [Four-dimensional disk embedding and Wall's conjecture](https://closedform.nishachay.tech/e/openai-math-2026-305/). ## Results (18) - [The Hilbert–Smith conjecture in every dimension](https://closedform.nishachay.tech/e/openai-math-2026-304/) - Entry 304 · Claims a proof of Hilbert–Smith: a locally compact group acting faithfully on a connected manifold is a Lie group. (Claimed, not checked) - [Four-dimensional disk embedding and Wall's conjecture](https://closedform.nishachay.tech/e/openai-math-2026-305/) - Entry 305 · Claims the two-generator free group is not good for 4D surgery, plus a counterexample to Wall's question. (Claimed, not checked) - [The purely cosmetic surgery conjecture](https://closedform.nishachay.tech/e/openai-math-2026-306/) - Entry 306 · Claims that two different surgeries on a nontrivial knot never give the same oriented three-dimensional space. (Claimed, not checked) - [Failure of rational injectivity for maximal coarse assembly](https://closedform.nishachay.tech/e/openai-math-2026-307/) - Entry 307 · Graph families where coarse assembly forgets a class of infinite order; Lean checks the reduced version. (Formal proof listed) - [Finite Smith–Toda complexes at every height](https://closedform.nishachay.tech/e/openai-math-2026-308/) - Entry 308 · Claims Smith–Toda complexes exist at every height if the prime may grow, with an explicit V(4) at the prime 1009. (Claimed, not checked) - [The Kervaire invariant problem at the prime three](https://closedform.nishachay.tech/e/openai-math-2026-309/) - Entry 309 · Claims to settle which odd-primary Kervaire classes survive at the prime three: stems 10, 106 and 322. (Claimed, not checked) - [Quillen's conjecture in rational homology](https://closedform.nishachay.tech/e/openai-math-2026-310/) - Entry 310 · Claims Quillen's 1978 conjecture on subgroup posets for every finite group and every prime, in a stronger homology form. (Claimed, not checked) - [The Hovey–Strickland and Chai conjectures](https://closedform.nishachay.tech/e/openai-math-2026-311/) - Entry 311 · Claims Chai's invariant-ideal conjecture at every prime and height, and with it the Hovey–Strickland classification. (Claimed, not checked) - [The Grothendieck homotopy hypothesis](https://closedform.nishachay.tech/e/openai-math-2026-312/) - Entry 312 · Grothendieck's algebraic ∞-groupoids capture all shapes of spaces, a paper claims, with its key step checked in Lean. (Formal proof listed) - [Finite generation for the K(n)-local sphere](https://closedform.nishachay.tech/e/openai-math-2026-313/) - Entry 313 · Claims every homotopy group of the K(n)-local sphere is finitely generated over the p-adic integers. (Claimed, not checked) - [Cyclic length and chromatic fixed-point loss](https://closedform.nishachay.tech/e/openai-math-2026-314/) - Entry 314 · Claims the exact chromatic loss between fixed points of p-group actions is a count of cyclic steps. (Claimed, not checked) - [The four-dimensional Singer conjecture](https://closedform.nishachay.tech/e/openai-math-2026-315/) - Entry 315 · Claims the Singer conjecture in dimension four: L²-Betti numbers of aspherical four-manifolds vanish off degree two. (Claimed, not checked) - [Curtis’s conjecture](https://closedform.nishachay.tech/e/openai-math-2026-316/) - Entry 316 · A paper claims to prove Curtis's 1975 conjecture: only η, ν, σ and Kervaire classes show up in mod-2 sphere homology. (Claimed, not checked) - [Thomason model structures in all strict higher dimensions](https://closedform.nishachay.tech/e/openai-math-2026-317/) - Entry 317 · Strict n-categories carry a Thomason model structure in every dimension, settling an Ara–Maltsiniotis conjecture. (Formal proof listed) - [Chromatic splitting: filtrations and counterexamples](https://closedform.nishachay.tech/e/openai-math-2026-318/) - Entry 318 · Five papers claim Hopkins' chromatic splitting conjecture fails in its strong and weak forms, and offer a filtered fix. (Claimed, not checked) - [Counterexamples to finite generation at chromatic height two](https://closedform.nishachay.tech/e/openai-math-2026-319/) - Entry 319 · A paper claims to disprove the Hahn–Wilson conjecture at height two, for every large enough prime. (Claimed, not checked) - [Nonhomeomorphic closed aspherical four-manifolds](https://closedform.nishachay.tech/e/openai-math-2026-320/) - Entry 320 · A paper claims two closed aspherical 4-manifolds with the same homotopy type but no homeomorphism, against Borel. (Claimed, not checked) - [A counterexample to Wall's finite D(2) problem](https://closedform.nishachay.tech/e/openai-math-2026-321/) - Entry 321 · A paper claims a negative answer to Wall's D(2) problem: a finite 3-complex that passes the test but has no 2-d model. 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