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.
a torus with some handles, etc.
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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