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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 ...
[10] An independent transversal (also called a rainbow-independent set or independent system of representatives ) is a transversal which is also an independent set of a given graph. To explain the difference in figurative terms, consider a faculty with m departments, where the faculty dean wants to construct a committee of m members, one member ...
In dynamical systems theory, an area of pure mathematics, a Morse–Smale system is a smooth dynamical system whose non-wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a transversality condition on the stable and unstable manifolds.
Download as PDF; Printable version; ... a notion in mathematics; Transversality theorem, a theorem in differential topology; See also ... at 10:22 (UTC). Text is ...
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.
Black literature is far too expansive to cover in just a month, especially if you look back through history at the works of luminaries like Langston Hughes, Toni Morrison, James Baldwin and Nikki ...
On the other hand, he showed that every integral cohomology class of positive degree on a smooth manifold has a positive multiple that is the class of a smooth submanifold. [6] Also, every integral cohomology class on a manifold can be represented by a "pseudomanifold", that is, a simplicial complex that is a manifold outside a closed subset of ...