Source / pinned edition
The Poincare Conjecture
Source of package cmi.poincare · claymath.org/wp-content/uploads/2022/06/poincare.pdf
- work
- urn:org:cmi:poincare#CMI_MILNOR_OFFICIAL_DESCRIPTION
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- claymath.org/wp-content/uploads/2022/06/poincare.pdf
- kind
- urn:org:cmi:poincare#treatise
CMI_MILNOR_EDITION
- edition
- urn:org:cmi:poincare#CMI_MILNOR_EDITION
- language
- en
- officiality
- official
- materialisation
- PINNED_UNOFFICIAL_COPY
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Publications
| URI | Type | documentHash | Retrieved |
|---|---|---|---|
| https://www.claymath.org/wp-content/uploads/2022/06/poincare.pdf | text/plain; charset=utf-8 | sha256:fe231dfcbc15f4b6e9282903bd50499cf82cfa4387d5c195b30d0783df461200 | 2026-09-17T00:00:00Z |
Fragments — 5
section2-false-theorem-1900 · defn · referenced by: 1
en · official · sha256:c94f2a3142ed30d78848752bd737241fb7fb64cd2cd87e5f9fb055ee8521dc96
False Theorem. Every compact polyhedral manifold with the homology of an n-dimensional sphere is actually homeomorphic to the n-dimensional sphere.Referencing norms: defines-homology-sphere-false-theorem
section2-icosahedral-counterexample-1904 · defn · referenced by: 1
en · official · sha256:c3f2d32ace7d520aa63ec9ab918deab8ef841fbb31dd1a00e6d8d5934f906008
This manifold meets Poincare's preliminary criterion: by the methods of homology theory, it cannot be distinguished from the three-dimensional sphere. However, he could prove that it is not a sphere by constructing a simple closed curve that cannot be deformed to a point within M^3.Referencing norms: names-icosahedral-counterexample
section1-named-conjecture · lemma · referenced by: 3
en · official · sha256:9488ebf66638b9d778b6950fe813b093de671c6e441929438a4ea7c52ec03d75
Since then, the hypothesis that every simply connected closed 3-manifold is homeomorphic to the 3-sphere has been known as the Poincare Conjecture.Referencing norms: PoincareConjectureStatement, poincare-identifies-conjecture, source-asserts-poincare
section1-question · lemma · referenced by: 1
en · official · sha256:bad8719d07b19c87b72c53cb43632fcaabb4620f9f784fb3b2c5b569dcdf7338
Question. If a compact three-dimensional manifold M^3 has the property that every simple closed curve within the manifold can be deformed continuously to a point, does it follow that M^3 is homeomorphic to the sphere S^3?Referencing norms: defines-simply-connected-test
title · defn · referenced by: 5
en · official · sha256:610074224084ac19a07f004276714e1dd82c27c0ddd5ae9c37d5769d91c000b0
THE POINCARE CONJECTUREReferencing norms: CmiPoincareSource, classified_as_millennium_problem, defines_notion, names_historical_result, poincare-classified
The hash beside the text is the sha256 of its exact bytes. It is the check that the text shown matches the one pinned in the package: a divergence fails the oracle’s static analysis.