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Topology is the study of the properties of space preserved under continuous deformations, including twisting and stretching. Topology originated from the study of geometry and set theory and has many branches today. Wolfram|Alpha has the knowledge and ability to handle multiple topological topics, like computing the homotopy groups of an n-sphere (algebraic topology) or visualizing a knot (geometric topology).

Homotopy Groups of Spheres

Compute the homotopy groups of an n-sphere.

Compute homotopy groups of a sphere:

Compute a specified homotopy group:

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