- #1
wofsy
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The Klein bottle, though unorientable, is nevertheless the boundary of a three manifold. It is easy to see how to construct this 3 manifold.
The projective plane is not a boundary of any manifold. How can we visualize this impossibility?
Is there a nice embedding of the projective plane in R^4? How about an embedding of the projective plane in Euclidean space so that it has constant curvature?
Same embedding question for the Klein bottle.
The projective plane is not a boundary of any manifold. How can we visualize this impossibility?
Is there a nice embedding of the projective plane in R^4? How about an embedding of the projective plane in Euclidean space so that it has constant curvature?
Same embedding question for the Klein bottle.