Statements (193)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
gptkb:chess_match |
| gptkbp:bfsLayer |
3
|
| gptkbp:bfsParent |
gptkb:Grigori_Perelman
gptkb:Henri_Poincaré |
| gptkbp:challenges |
gptkb:Mathematician
mathematical research topologists nan complexity of 3-manifolds |
| gptkbp:command_structure |
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
|
| gptkbp:consequences |
characterization of the 3-sphere
|
| gptkbp:field |
gptkb:Mathematician
gptkb:television_channel |
| gptkbp:first_awarded |
gptkb:Clay_Millennium_Prize
|
| gptkbp:focuses_on |
mathematical education
mathematical exploration |
| gptkbp:has_impact_on |
mathematical physics
3-manifolds |
| gptkbp:has_influence_on |
further research in topology
|
| gptkbp:has_method |
gptkb:Ricci_flow_with_surgery
|
| gptkbp:has_programs |
gptkb:physicist
|
| gptkbp:historical_debate |
gptkb:Grigori_Perelman
|
| gptkbp:historical_event |
gptkb:Mathematician
|
| gptkbp:historical_significance |
in mathematics
|
| https://www.w3.org/2000/01/rdf-schema#label |
Poincaré conjecture
|
| gptkbp:influenced_by |
Riemannian geometry
Algebraic topology |
| gptkbp:is_a |
gptkb:Millennium_Prize_Problem
gptkb:theorem gptkb:concept gptkb:chess_match geometric conjecture topological property mathematical exploration theoretical exploration mathematical inquiry open problem problem in topology mathematical challenge theoretical challenge geometric exploration theoretical inquiry topological statement closed 3-manifold property closed manifold property conjecture about 3-manifolds geometric challenge geometric inquiry homeomorphism property hypothesis about spaces simply connected property statement about geometric structures theorem in topology topological challenge topological conjecture topological exploration topological inquiry |
| gptkbp:is_a_center_for |
gptkb:television_channel
the field of topology |
| gptkbp:is_a_solution_for |
gptkb:Grigori_Perelman
gptkb:Ricci_flow the early 21st century |
| gptkbp:is_about |
3-dimensional manifolds
|
| gptkbp:is_associated_with |
homeomorphism
Henri Poincaré's work |
| gptkbp:is_cited_in |
mathematical discussions
|
| gptkbp:is_compared_to |
the statement that every simply connected, closed 3-manifold is homeomorphic to the 3-sphere
the 3-dimensional sphere |
| gptkbp:is_considered |
one of the most famous problems in mathematics
a major achievement in mathematics one of the seven Millennium Prize Problems |
| gptkbp:is_critical_for |
the field of topology
|
| gptkbp:is_discussed_in |
mathematical literature
the topology of higher dimensions |
| gptkbp:is_essential_for |
gptkb:Mathematician
mathematical research one of the seven Millennium Prize Problems |
| gptkbp:is_explored_in |
advanced mathematics courses
|
| gptkbp:is_fundamental_to |
modern topology
3-manifold topology topological studies |
| gptkbp:is_influential_in |
mathematical topology
|
| gptkbp:is_part_of |
geometric topology
|
| gptkbp:is_referenced_in |
academic papers
|
| gptkbp:is_related_to |
homotopy theory
3-manifolds differential topology the study of manifolds |
| gptkbp:is_standardized_by |
Geometrization conjecture
|
| gptkbp:is_studied_in |
over a century
topologists many mathematicians |
| gptkbp:issues |
gptkb:television_channel
3-manifolds nan |
| gptkbp:key |
differential geometry
modern topology |
| gptkbp:key_issues |
the study of manifolds
|
| gptkbp:named_after |
gptkb:Henri_Poincaré
|
| gptkbp:notable_achievement |
gptkb:Mathematician
mathematical history |
| gptkbp:notable_album |
1904
|
| gptkbp:notable_event |
a conjecture in mathematics
|
| gptkbp:part_of |
geometric topology
|
| gptkbp:performance |
topological research
|
| gptkbp:proposed_by |
gptkb:Henri_Poincaré
1904 |
| gptkbp:published_by |
gptkb:2003
1904 |
| gptkbp:related_concept |
gptkb:Klein_bottle
gptkb:Brouwer_fixed-point_theorem gptkb:Heegaard_splitting Riemannian geometry algebraic topology homotopy theory topological dimension topological groups topological spaces fundamental group homology homotopy homotopy equivalence simplicial complexes topological invariants metric spaces Euler characteristic knot theory topological classification geometric topology smooth manifolds Cohomology theory Morse theory smooth structures homotopy type theory topological equivalence compact manifolds differential topology non-orientable surfaces torus projective plane cell complex surgery theory fiber bundles topological manifolds simplicial complex diffeomorphism topological invariance homotopy groups Chern classes cellular homology local homology manifold theory manifold topology simplicial homology spherical topology topological classification of manifolds topological classification of surfaces topological embeddings Dehn surgery Seifert fibered spaces algebraic topology techniques cell complexes global topology |
| gptkbp:related_to |
gptkb:Ricci_flow
3-manifolds Geometrization conjecture |
| gptkbp:research |
manifold theory
|
| gptkbp:resulted_in |
gptkb:2003
gptkb:2006 topological studies |
| gptkbp:significance |
gptkb:Mathematician
fundamental in the study of topology fundamental in the study of 3-manifolds. |
| gptkbp:significant_event |
the study of topology
theory of manifolds |
| gptkbp:state |
every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
every simply connected, closed 3-manifold is homeomorphic to the 3-sphere |
| gptkbp:subject |
mathematical analysis
mathematical education mathematical conferences theoretical mathematics mathematicians worldwide mathematical historians mathematical lectures mathematical debate mathematical inquiry |
| gptkbp:technique |
gptkb:Ricci_flow_with_surgery
|
| gptkbp:theme |
topological research
|
| gptkbp:theory |
the topology of 3-dimensional spaces
|
| gptkbp:type |
topological property
|
| gptkbp:varieties |
topological
|
| gptkbp:year |
gptkb:2003
|