topology exam

[annathyst]

Good enough for partial credit. I didn't like Problem 2.
Close enough to being done that I can go to sleep and then hand it in in sure knowledge that I'll pass.

Night.

Comments

[annathyst]

Not only is it a closed surface, you can get it by doing the same kind of thing you'd do with a square to turn it into a torus. You join the top and bottom edges like you would in a torus, but you join the left and right edges with a half-twist, so the bottom of one is joined to the top of the other and vice versa.

Don't try to do it, you can't in three dimensions :) But the resulting identification space is definitely a Klein bottle.

[slab]

Mmm... forbidden Klein bottle...