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gptkbp:instanceOf
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gptkb:mathematical_concept
3-manifold
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gptkbp:appearsIn
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low-dimensional topology
singularity theory
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gptkbp:arisesAs
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link of singularity
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gptkbp:canBe
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exotic sphere
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gptkbp:definedIn
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gptkb:Brieskorn
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gptkbp:describedBy
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intersection of complex hypersurfaces
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gptkbp:dimensions
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3
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gptkbp:example
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gptkb:Σ(2,3,5)_(Poincaré_sphere)
exotic 3-sphere
Σ(2,3,7)
Σ(3,4,5)
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gptkbp:hasApplication
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study of smooth structures on spheres
counterexamples in topology
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gptkbp:hasEquation
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z1^a + z2^b + z3^c = 0 intersected with unit sphere in C^3
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gptkbp:hasInvariant
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gptkb:Casson_invariant
gptkb:Rokhlin_invariant
homology group same as S^3
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gptkbp:hasProperty
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gptkb:Riemannian_manifold
compact
oriented
closed manifold
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gptkbp:hasSpecialCase
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gptkb:Poincaré_homology_sphere
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https://www.w3.org/2000/01/rdf-schema#label
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Brieskorn sphere
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gptkbp:isA
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gptkb:Seifert_fiber_space
homology sphere
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gptkbp:namedAfter
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gptkb:Egon_Brieskorn
|
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gptkbp:notHomeomorphicTo
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standard 3-sphere (for some examples)
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gptkbp:parameter
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integers a, b, c > 1
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|
gptkbp:studiedIn
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gptkb:topology
differential geometry
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gptkbp:bfsParent
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gptkb:Egbert_Brieskorn
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gptkbp:bfsLayer
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6
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