# Category: Differential structures

Hilbert's fifth problem
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups. The theory of Lie gr
Exotic sphere
In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a s
Rokhlin's theorem
In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, closed 4-manifold M has a spin structure (or, equivalently, the second Stiefelâ€“Whitney class vanishes), t
Differential structure
In 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 some addition
Exotic R4
In mathematics, an exotic is a differentiable manifold that is homeomorphic (i.e. shape preserving) but not diffeomorphic (i.e. non smooth) to the Euclidean space The first examples were found in 1982
Flat function
In mathematics, especially real analysis, a flat function is a smooth function all of whose derivatives vanish at a given point . The flat functions are, in some sense, the antitheses of the analytic
Clutching construction
In topology, a branch of mathematics, the clutching construction is a way of constructing fiber bundles, particularly vector bundles on spheres.