Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Thom_conjecture> ?p ?o. }
Showing items 1 to 24 of
24
with 100 items per page.
- Thom_conjecture abstract "In mathematics, a smooth algebraic curve in the complex projective plane, of degree , has genus given by the formula .The Thom conjecture, named after French mathematician René Thom, states that if is any smoothly embedded connected curve representing the same class in homology as , then the genus of satisfies .In particular, C is known as a genus minimizing representative of its homology class. It was first proved by Kronheimer–Mrowka in October 1994, using the then-new Seiberg–Witten invariants. Assuming that has nonnegative self intersection number this was generalizes to Kähler manifolds (an example being the complex projective plane) by Morgan–Szabó–Taubes, also using the then-new Seiberg–Witten invariants. There is at least one generalization of this conjecture, known as the symplectic Thom conjecture (which is now a theorem, as proved for example by Ozsváth and Szabó in 2000). It states that a symplectic surface of a symplectic 4-manifold is genus minimizing within its homology class. This would imply the previous result because algebraic curves (complex dimension 1, real dimension 2) are symplectic surfaces within the complex projective plane, which is a symplectic 4-manifold.".
- Thom_conjecture wikiPageID "3846986".
- Thom_conjecture wikiPageRevisionID "544275718".
- Thom_conjecture hasPhotoCollection Thom_conjecture.
- Thom_conjecture subject Category:4-manifolds.
- Thom_conjecture subject Category:Algebraic_surfaces.
- Thom_conjecture subject Category:Conjectures.
- Thom_conjecture subject Category:Four-dimensional_geometry.
- Thom_conjecture type AlgebraicSurfaces.
- Thom_conjecture type Artifact100021939.
- Thom_conjecture type Object100002684.
- Thom_conjecture type PhysicalEntity100001930.
- Thom_conjecture type Surface104362025.
- Thom_conjecture type Whole100003553.
- Thom_conjecture comment "In mathematics, a smooth algebraic curve in the complex projective plane, of degree , has genus given by the formula .The Thom conjecture, named after French mathematician René Thom, states that if is any smoothly embedded connected curve representing the same class in homology as , then the genus of satisfies .In particular, C is known as a genus minimizing representative of its homology class.".
- Thom_conjecture label "Thom conjecture".
- Thom_conjecture label "Thom-Vermutung".
- Thom_conjecture sameAs Thom-Vermutung.
- Thom_conjecture sameAs m.0b31xy.
- Thom_conjecture sameAs Q2421730.
- Thom_conjecture sameAs Q2421730.
- Thom_conjecture sameAs Thom_conjecture.
- Thom_conjecture wasDerivedFrom Thom_conjecture?oldid=544275718.
- Thom_conjecture isPrimaryTopicOf Thom_conjecture.