About: Transversality theorem

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In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result that describes the transverse intersection properties of a smooth family of smooth maps. It says that transversality is a generic property: any smooth map , may be deformed by an arbitrary small amount into a map that is transverse to a given submanifold . Together with the Pontryagin–Thom construction, it is the technical heart of cobordism theory, and the starting point for surgery theory. The finite-dimensional version of the transversality theorem is also a very useful tool for establishing the genericity of a property which is dependent on a finite number of real parameters and which is expressible using a system of nonlinear equat

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rdf:type	yago:WikicatMathematicalTheorems yago:WikicatTheoremsInDifferentialTopology yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Transversalitätssatz (de) Transversality theorem (en)
rdfs:comment	Der Transversalitätssatz ist ein auf René Thom zurückgehender Satz der Differentialtopologie, der die Grundlage für zahlreiche topologische Konstruktionen wie zum Beispiel die , die Kobordismustheorie, sowie die Definition von Schnittzahlen und Verschlingungszahlen bildet. (de) In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result that describes the transverse intersection properties of a smooth family of smooth maps. It says that transversality is a generic property: any smooth map , may be deformed by an arbitrary small amount into a map that is transverse to a given submanifold . Together with the Pontryagin–Thom construction, it is the technical heart of cobordism theory, and the starting point for surgery theory. The finite-dimensional version of the transversality theorem is also a very useful tool for establishing the genericity of a property which is dependent on a finite number of real parameters and which is expressible using a system of nonlinear equat (en)
dcterms:subject	Differential geometry Theorems in differential topology
Wikipage page ID	22667049 (xsd:integer)
Wikipage revision ID	1012856223 (xsd:integer)
Link from a Wikipage to another Wikipage	René Thom Thom space Transversality (mathematics) Differential geometry Generic property Commentarii Mathematici Helvetici Jet (mathematics) France Differential topology Theorems in differential topology Surgery theory Manifold Fredholm operator John Mather (mathematician) Cobordism theory
Link from a Wikipage to an external page	https://archive.org/details/geometricalmetho0000arno_o8o1 https://archive.org/details/springer_10.1007-978-1-4684-9449-5
sameAs	Transversality theorem Transversality theorem Transversality theorem Transversality theorem Transversality theorem
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Citation_needed dbt:Cite_book dbt:Cite_journal dbt:Short_description
has abstract	Der Transversalitätssatz ist ein auf René Thom zurückgehender Satz der Differentialtopologie, der die Grundlage für zahlreiche topologische Konstruktionen wie zum Beispiel die , die Kobordismustheorie, sowie die Definition von Schnittzahlen und Verschlingungszahlen bildet. (de) In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result that describes the transverse intersection properties of a smooth family of smooth maps. It says that transversality is a generic property: any smooth map , may be deformed by an arbitrary small amount into a map that is transverse to a given submanifold . Together with the Pontryagin–Thom construction, it is the technical heart of cobordism theory, and the starting point for surgery theory. The finite-dimensional version of the transversality theorem is also a very useful tool for establishing the genericity of a property which is dependent on a finite number of real parameters and which is expressible using a system of nonlinear equations. This can be extended to an infinite-dimensional parametrization using the infinite-dimensional version of the transversality theorem. (en)
prov:wasDerivedFrom	wikipedia-en:Transversality_theorem?oldid=1012856223&ns=0
page length (characters) of wiki page	8348 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Transversality_theorem
is Link from a Wikipage to another Wikipage of	List of XML and HTML character entity references ⋔ ⫛ Thom space Transversality (mathematics) Transversality Jet (mathematics) Whitney conditions Sphere theorem (3-manifolds) Transverse knot Thom’s transversality theorem Thom transversality theorem
is Wikipage redirect of	⋔ ⫛ Thom’s transversality theorem Thom transversality theorem
is foaf:primaryTopic of	wikipedia-en:Transversality_theorem

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