Transversality (other)

	Transversality (other) Transversality may refer to: * Transversality (mathematics), a notion in mathematics * Transversality theorem, a theorem in differential topology See also * Transverse (other) Transversal (other) Transversal may refer to: Transversal (combinatorics), a set containing exactly one member of each of several other sets * Transversal (geometry), a line that intersects two or more lines at different points * Transversal (instrument making), a ... * Longitudinal (other) {{Mathematical disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Transversality (mathematics) 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 intersection. Definition Two submanifolds of a given finite-dimensional smooth manifold are said to intersect transversally if at every point of intersection, their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point. Manifolds that do not intersect are vacuously transverse. If the manifolds are of complementary dimension (i.e., their dimensions add up to the dimension of the ambient space), the condition means that the tangent space to the ambient manifold is the direct sum of the two smaller tangent spaces. If an intersection is transverse, then the intersection will be a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Transversality Theorem 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 f\colon X\rightarrow Y, may be deformed by an arbitrary small amount into a map that is transverse to a given submanifold Z \subseteq Y. 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. Finite-dimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Transverse (other) Transverse may refer to: Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle Transverse flute, a flute that is held horizontally * Transverse force (or ''Euler force''), the tangential force that is felt in reaction to any angular acceleration Transverse mass, a particle physics quantity Transverse plane, the plane orthogonal to the anteroposterior or oral-aboral axis Transverse rotors, a type of rotorcraft in which there are two rotors mounted side by side Transverse wave, a wave that causes a disturbance in the medium perpendicular to the direction it advances Transverse Island, an island on the east side of Stefansson Bay, off the coast of Enderby Land See also Transversal (other) Transversality (other) Transversality may refer to: Transversality (mathematics), a notion in mathematics * Transversality theorem, a theorem in differential topology See also * Transverse (disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Transversal (other) Transversal may refer to: * Transversal (combinatorics), a set containing exactly one member of each of several other sets * Transversal (geometry), a line that intersects two or more lines at different points * Transversal (instrument making), a technique for subdividing graduations * Transversal Corporation, a software company * Transversal plane, a geometric concept * Transversal, relating to the transverse plane The transverse plane (also known as the horizontal plane, axial plane and transaxial plane) is an anatomical plane that divides the body into superior and inferior sections. It is perpendicular to the coronal and sagittal planes. List of c ... in anatomy See also * Transverse (other) * Transversality (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]