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Current Problems in Topology

Instructor: Rustam Sadykov
Course: Current Problems in Topology, M124

sphere eversion

A smooth manifold is a topological space each point of which has a neighborhood resembling a Euclidean space. A smooth manifold can be thought of as a high dimensional generalization of a surface. Topology and geometry of smooth manifolds is an important rapidly developing branch of topology.

This is an introductory course designed to provide students with basic fundamental concepts in the theory.

The picture at the top is a snapshot from a computer-animated video Outside In created by the Geometry Center. The video explains a process of eversion of the standard sphere in the 3-space without creating creases.