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In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of ...
There are more powerful statements (collectively known as transversality theorems) that imply the parametric transversality theorem and are needed for more advanced applications. Informally, the "transversality theorem" states that the set of mappings that are transverse to a given submanifold is a dense open (or, in some cases, only a dense G ...
In mathematics, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, introduced by Eugenio Bertini.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
The embedded manifold together with the isomorphism class of the normal bundle actually encodes the same information as the cobordism class []. This can be shown [ 2 ] by using a cobordism W {\displaystyle W} and finding an embedding to some R N W + n × [ 0 , 1 ] {\displaystyle \mathbb {R} ^{N_{W}+n}\times [0,1]} which gives a homotopy class ...
All India Secondary School Examination, commonly known as the class 10th board exam, is a centralized public examination that students in schools affiliated with the Central Board of Secondary Education, primarily in India but also in other Indian-patterned schools affiliated to the CBSE across the world, taken at the end of class 10. The board ...
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In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.