: Mathematics: exotic sphere

topology > algebraic topology > manifold > differentiable manifold > exotic sphere

geometry > topological space > manifold > differentiable manifold > exotic sphere

geometry > differential geometry > differentiable manifold > exotic sphere

topology > differential topology > differentiable manifold > exotic sphere

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 sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name "exotic").
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Exotic_sphere)

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