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Topological Types

This is where we will classify compact connected 2-manifolds topologically. An orientable 2-manifold is one for which all paths are orientation-preserving. A non-orientable 2-manifold contains at least one orientation-reversing path; equivalently, it contains a Möbius band.

Orientable Surfaces

The sphere
The torus
a torus with some handles, etc.

Non-orientable Surfaces

The Klein bottle
The projective plane


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Created: Jun 27 1995 ---- Last modified: Sun Dec 3 21:16:59 1995
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