Thurston's geometrization theorem
GPTKB entity
Statements (69)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:bfsLayer |
4
|
| gptkbp:bfsParent |
gptkb:William_Thurston
|
| gptkbp:applies_to |
mathematical modeling
3-manifolds |
| gptkbp:based_on |
the concept of geometric structures
|
| gptkbp:challenges |
gptkb:University
gptkb:physicist prove understand |
| gptkbp:discovered_by |
gptkb:Grigori_Perelman
|
| gptkbp:examines |
gptkb:Mathematician
topologists mathematical seminars topological studies |
| gptkbp:has_impact_on |
the Poincaré conjecture
|
| gptkbp:has_programs |
gptkb:physicist
|
| https://www.w3.org/2000/01/rdf-schema#label |
Thurston's geometrization theorem
|
| gptkbp:is_a |
gptkb:church
|
| gptkbp:is_analyzed_in |
research articles
|
| gptkbp:is_associated_with |
differential geometry
|
| gptkbp:is_cited_in |
academic papers
|
| gptkbp:is_connected_to |
the study of manifolds
3-manifold theory |
| gptkbp:is_considered |
a major achievement in mathematics
a cornerstone of modern topology |
| gptkbp:is_described_as |
topology textbooks
|
| gptkbp:is_discussed_in |
conferences
experts mathematical literature mathematical forums mathematical theorists |
| gptkbp:is_essential_for |
understanding 3-dimensional topology
|
| gptkbp:is_explored_in |
gptkb:academic_research
geometric constructions mathematical proofs geometric analysis graduate studies |
| gptkbp:is_fundamental_to |
the study of manifolds
|
| gptkbp:is_influenced_by |
previous work in topology
|
| gptkbp:is_influential_in |
modern geometry
|
| gptkbp:is_linked_to |
knot theory
the study of topology the study of shapes |
| gptkbp:is_part_of |
theoretical frameworks
theoretical mathematics geometric topology the study of geometric structures |
| gptkbp:is_recognized_by |
the mathematical community
|
| gptkbp:is_reflected_in |
topological invariants
geometric models geometric proofs geometric theories |
| gptkbp:is_related_to |
gptkb:television_channel
gptkb:Ricci_flow the study of surfaces hyperbolic geometry |
| gptkbp:is_standardized_by |
the uniformization theorem
|
| gptkbp:is_studied_in |
mathematics courses
|
| gptkbp:is_supported_by |
geometric intuition
|
| gptkbp:is_tested_for |
examples of 3-manifolds
|
| gptkbp:is_used_in |
mathematical research
|
| gptkbp:is_utilized_in |
computer simulations
mathematical proofs mathematical applications theoretical explorations |
| gptkbp:proposed_by |
gptkb:William_Thurston
|
| gptkbp:published_by |
the 1980s
|
| gptkbp:state |
every closed 3-manifold can be decomposed into pieces that have geometric structures
|