I'm giving a presentation about orientable surfaces (as a student project) and I was wondering what I should talk about. The presentation should be 20-30 min long.
I've been thinking maybe something like this:
1) definition of a surface
2) what does orientable mean (orientable vs. oriented)
And then I'm a bit lost. In the general topology course last year, classification of compact surfaces and covering maps were mentioned but I don't much about either and I don't know if it has anything to do with orientability of surfaces.
In this class, algebraic topology, we're going to learn about cell complexes and homology, but I don't think that has anything to do with orientability either.
Question: what is an interesting fact or theorem that I should definitely mention in this presentation?
Many thanks for your help!
1) definition of surface and manifold
2) definition of orientable (with paper moebius strip)
3) classification of compact orientable surfaces
Just in case anyone reads this post later, they might use this to get inspiration. I had also prepared material about homology but the professor said homology was going to be discussed towards the very end of the lecture so I did not present what I had prepared.