Hopf fibration
Videos
In differential topology, the Hopf fibration describes a 3-sphere in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Te
Pairwise linked keyrings mimic part of the Hopf fibration.
Homotopy groups of spheres
Videos
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, whic
A homotopy from a circle around a sphere down to a single point