Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
3-manifold
homology sphere |
| gptkbp:alsoKnownAs |
gptkb:Poincaré_homology_sphere
|
| gptkbp:BrieskornParameters |
(2,3,5)
|
| gptkbp:canBe |
gluing opposite faces of a dodecahedron after a 1/10 turn
|
| gptkbp:describedBy |
gptkb:Brieskorn_sphere
gptkb:Seifert_fiber_space dodecahedral space |
| gptkbp:directionA |
orientable
|
| gptkbp:fundamentalGroup |
gptkb:binary_icosahedral_group
|
| gptkbp:fundamentalGroupOrder |
120
|
| gptkbp:hasFirstHomologyGroup |
trivial
|
| gptkbp:hasHeegaardGenus |
2
|
| gptkbp:hasSecondHomologyGroup |
trivial
|
| gptkbp:hasThirdHomologyGroup |
Z
|
| gptkbp:heldBy |
first discovered example of a homology sphere not homeomorphic to the 3-sphere
|
| https://www.w3.org/2000/01/rdf-schema#label |
Σ(2,3,5) (Poincaré sphere)
|
| gptkbp:isBrieskornSphere |
yes
|
| gptkbp:isSolutionTo |
Poincaré conjecture (as a counterexample to naive formulation)
|
| gptkbp:namedAfter |
gptkb:Henri_Poincaré
|
| gptkbp:universalCover |
gptkb:3-sphere
|
| gptkbp:bfsParent |
gptkb:Brieskorn_sphere
|
| gptkbp:bfsLayer |
7
|