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Topology Joke

Henry Segerman

Surface: 

Locally looks like the plane

Text

Manifold: 

Locally looks like R^n

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What Surface do they live on?

Can you actually make it the sphere?

 Cutting the sphere into polygons

Conjecture: 

Draw a graph on a sphere.

Let V be the number of vertices

Let E be the number of edges

Let F be the number of faces

Then:

V-E+F=2