mathematics, an n-dimensional differential structure (or differentiable structure) on a set M makes M into an n-dimensional differential manifold, which is a topological...

manifold with a globally defined differential structure. Any topological manifold can be given a differential structure locally by using the homeomorphisms...

comparison differential topology is concerned with coarser properties, such as the number of holes in a manifold, its homotopy type, or the structure of its...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

metric structures (geometries), orders, graphs, events, Setoids, differential structures, and categories. Sometimes, a set is endowed with more than one...

preserved. Differential geometry views a plane as a 2-dimensional real manifold, a topological plane which is provided with a differential structure. Again...

spaces. A diffeomorphism is an isomorphism of spaces equipped with a differential structure, typically differentiable manifolds. A symplectomorphism is an isomorphism...

by adding structure to a topological manifold (e.g. differentiable manifolds are topological manifolds equipped with a differential structure). Every manifold...

the differential structure of smooth manifolds via de Rham cohomology, or Čech or sheaf cohomology to investigate the solvability of differential equations...

inherits the differential structure of F. Suppose F and G are differential fields satisfying Con(F) = Con(G), and G is an elementary differential extension...

the natural differential structure of R n {\displaystyle \mathbb {R} ^{n}} (that is, if they are diffeomorphisms), the differential structure transfers...

In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the...

notation may be applied with any tensors, operations relating to a differential structure are only applicable to tensor fields. Where needed, the notation...

topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used to capture information about...

systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of...

geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra A {\displaystyle A} over a field...

the image subset S {\displaystyle S} together with a topology and differential structure such that S {\displaystyle S} is a manifold and the inclusion f...

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other...

Laurence R. (1986). "A universal smoothing of four-space". Journal of Differential Geometry. 24 (1): 69–78. doi:10.4310/jdg/1214440258. ISSN 0022-040X....

includes a variable conductance term that is determined using the differential structure of the image, such that the heat does not propagate over the edges...

around its edges. The sedimentary rocks composing this structure dip outward at 10–20°. Differential erosion of resistant layers of quartzite has created...

In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...

This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...

In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal...

In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

In mathematics, a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients...

In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...

mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators...

results of Donaldson theory depend therefore on the manifold having a differential structure, and are largely false for topological 4-manifolds. Many of the...