| dbo:abstract |
En mathématiques, l'étude qualitative des champs de vecteurs sur les n-sphères est une question classique de topologie différentielle, initiée par le théorème de la boule chevelue, et par les premiers travaux de classification des algèbres à division. Plus précisément, la question est de savoir combien de champs de vecteurs linéairement indépendants peuvent exister sur une n-sphère ; elle fut résolue en 1962 par Frank Adams. (fr) In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras. Specifically, the question is how many linearly independent smooth nowhere-zero vector fields can be constructed on a sphere in N-dimensional Euclidean space. A definitive answer was provided in 1962 by Frank Adams. It was already known, by direct construction using Clifford algebras, that there were at least ρ(N)-1 such fields (see definition below). Adams applied homotopy theory and topological K-theory to prove that no more independent vector fields could be found. Hence ρ(N)-1 is the exact number of pointwise linearly independent vector fields that exist on an (N-1)-dimensional sphere. (en) |
| dbo:wikiPageExternalLink |
https://archive.org/details/topologicalgeome0000port https://archive.org/details/topologicalgeome0000port/page/336 https://ocw.mit.edu/courses/mathematics/18-915-graduate-topology-seminar-kan-seminar-fall-2014/math-talks/MIT18_915F14_Steenrod.pdf |
| dbo:wikiPageID |
3100908 (xsd:integer) |
| dbo:wikiPageLength |
4905 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1124430655 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Power_of_two dbr:Scalar_matrix dbr:Beno_Eckmann dbr:Hurwitz_problem dbc:Theorems_in_topology dbr:Mathematics dbr:Matrix_(mathematics) dbr:Tangent_bundle dbr:Clifford_algebra dbr:Frank_Adams dbr:Hairy_ball_theorem dbr:Orthonormal_basis dbr:Theoretical_physics dbr:Division_algebra dbr:Linear_independence dbr:Adolf_Hurwitz dbc:Differential_topology dbr:Euclidean_space dbr:Exotic_sphere dbr:Differential_topology dbr:Gram–Schmidt_process dbr:Quadratic_form dbr:Topological_K-theory dbr:Johann_Radon dbr:Coding_theory dbr:Homotopy_theory dbr:Orthogonal_matrix dbr:Hypersphere dbr:Similarity_transformation_(geometry) dbr:Poincaré–Hopf_index_theorem |
| dbp:wikiPageUsesTemplate |
dbt:Cite_book dbt:Cite_web dbt:More_citations_needed dbt:OEIS dbt:Reflist dbt:Short_description |
| dcterms:subject |
dbc:Theorems_in_topology dbc:Differential_topology |
| gold:hypernym |
dbr:Problem |
| rdf:type |
yago:WikicatTheoremsInTopology yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 dbo:Disease yago:Statement106722453 yago:Theorem106752293 |
| rdfs:comment |
En mathématiques, l'étude qualitative des champs de vecteurs sur les n-sphères est une question classique de topologie différentielle, initiée par le théorème de la boule chevelue, et par les premiers travaux de classification des algèbres à division. Plus précisément, la question est de savoir combien de champs de vecteurs linéairement indépendants peuvent exister sur une n-sphère ; elle fut résolue en 1962 par Frank Adams. (fr) In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras. (en) |
| rdfs:label |
Champs de vecteurs sur une sphère (fr) Vector fields on spheres (en) |
| owl:sameAs |
freebase:Vector fields on spheres yago-res:Vector fields on spheres wikidata:Vector fields on spheres dbpedia-fr:Vector fields on spheres https://global.dbpedia.org/id/4xbwJ |
| prov:wasDerivedFrom |
wikipedia-en:Vector_fields_on_spheres?oldid=1124430655&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Vector_fields_on_spheres |
| is dbo:knownFor of |
dbr:Johann_Radon |
| is dbo:wikiPageRedirects of |
dbr:Radon-Hurwitz_number dbr:Radon-Hurwitz_numbers dbr:Radon–Hurwitz_number dbr:Hurwitz-Radon_theorem dbr:Hurwitz–Radon_theorem |
| is dbo:wikiPageWikiLink of |
dbr:Algebraic_topology dbr:Hurwitz's_theorem_(composition_algebras) dbr:Frank_Adams dbr:Hairy_ball_theorem dbr:3-sphere dbr:Adolf_Hurwitz dbr:Topological_K-theory dbr:Johann_Radon dbr:Séminaire_Nicolas_Bourbaki_(1960–1969) dbr:Stunted_projective_space dbr:Radon-Hurwitz_number dbr:Radon-Hurwitz_numbers dbr:Radon–Hurwitz_number dbr:Hurwitz-Radon_theorem dbr:Hurwitz–Radon_theorem |
| is dbp:knownFor of |
dbr:Johann_Radon |
| is foaf:primaryTopic of |
wikipedia-en:Vector_fields_on_spheres |