AlgTop6: Non-orientable surfaces---the Mobius band

A surface is non-orientable if there is no consistent notion of right handed versus left handed on it. The simplest example is the Mobius band, a twisted strip with one side, and one edge. An important deformation gives what we call a crosscap.

This is the sixth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW.

[alfredorestrepo]

On minute 9:42, you might say that the x axis still points to the right but now the y axis points downwards.
On minute 41:15 of the video, in the sudanese surface construction, I´m not sure you can connect the two halves.

[alfredorestrepo]

On minute 9:42, you might say that the x axis still points to the right but now the y axis points downwards.

[ProfessorApothecary]

Dr. Wildberger, due to the chirality of the Möbius strip, does gluing mirrored crosscaps to the 2-sphere act idempotently on it? Wouldn't they "cancel out, " in a sense?

[georgeorfanidis]

elementary particles have orientation (left-handed or right handed) on experiment of large distance particles one day might show something.

[jursmin]

I agree with your first statement, but I think that the sudanese surface construction is right. Its really hard to imagine. This might help: /watch?v=ZXpF4YeAWDQ