Is a non-orientable surface a kind of manifold?

Question

An example of a non-orientable surface is the Moebius Strip. Iam just curious whether it is indeed a manifold by definition.

score 2 · Answer 1 · answered Jan 10 '14 at 19:08

Yes: a Möbius band is a manifold.

There are both orientable and non-orientable manifolds. The Klein bottle and the real projective plane are two other examples of non-orientable surfaces.

The definition of a manifold is a local one. The definition of orientability is a global one.

score 1 · Answer 2 · answered Jan 10 '14 at 19:08

1

Yes, it is an open manifold. Orientability has nothing to do with it...

answered Jan 10 '14 at 19:08

Igor Rivin

score 1 · Answer 3 · answered Jan 10 '14 at 19:09

1

Yes, as a manifold or as a $\partial$-manifold, of two cases.

answered Jan 10 '14 at 19:09

janmarqz

3 Answers3