Thurston's geometrization conjecture
GPTKB entity
Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:applies_to |
3-manifolds
|
| gptkbp:challenges |
prove
understand fully students of topology |
| gptkbp:has_applications_in |
gptkb:Physics
|
| gptkbp:has_implications_for |
the study of 3-manifolds
|
| https://www.w3.org/2000/01/rdf-schema#label |
Thurston's geometrization conjecture
|
| gptkbp:is_analyzed_in |
research papers
|
| gptkbp:is_associated_with |
the study of manifolds
|
| gptkbp:is_cited_in |
many mathematical papers
|
| gptkbp:is_connected_to |
gptkb:Ricci_flow
|
| gptkbp:is_considered |
a cornerstone of modern topology
a major result in mathematics a significant achievement in mathematics. |
| gptkbp:is_considered_by |
gptkb:Mathematician
|
| gptkbp:is_debated_in |
gptkb:Grigori_Perelman
|
| gptkbp:is_discussed_in |
gptkb:academic_journals
mathematical literature mathematical seminars conferences on topology |
| gptkbp:is_examined_in |
topological studies
topological research |
| gptkbp:is_explored_in |
differential geometry
geometric structures graduate studies topological courses |
| gptkbp:is_fundamental_to |
the field of topology
the understanding of 3-dimensional spaces |
| gptkbp:is_influenced_by |
previous mathematical theories
|
| gptkbp:is_influential_in |
modern geometry
|
| gptkbp:is_linked_to |
the study of hyperbolic manifolds
the classification of 3-manifolds the study of geometric structures on manifolds |
| gptkbp:is_part_of |
geometric topology
the history of mathematics theoretical frameworks in mathematics |
| gptkbp:is_recognized_as |
a breakthrough in mathematics
|
| gptkbp:is_reflected_in |
the development of geometric topology
the work of mathematicians like Perelman |
| gptkbp:is_related_to |
gptkb:topology
knot theory hyperbolic geometry |
| gptkbp:is_standardized_by |
gptkb:Poincaré_conjecture
|
| gptkbp:is_supported_by |
various mathematical proofs
|
| gptkbp:key |
solving problems in geometry
|
| gptkbp:proposed_by |
gptkb:William_Thurston
|
| gptkbp:state |
Every closed 3-manifold can be decomposed into pieces that have geometric structures.
|
| gptkbp:was_akey_figure_in |
mathematical physics
|
| gptkbp:was_conjectured_in |
gptkb:1980s
|
| gptkbp:bfsParent |
gptkb:William_Thurston
|
| gptkbp:bfsLayer |
6
|