BACKGROUND INFORMATION

Information needed to understand the proof.

TWO TOPICS

Key concepts in these two areas of math are used in the proof of the theorem. On each of these pages, the concepts are introduced.

TOPOLOGY

Topology concerns with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or pass-ing through itself.

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DIFFERENTIAL GEOMETRY

Differential geometry studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra.