Ok I see that's actually pretty simple. I guess I was thinking that integrating something like a line in R^3 should be dl (like a 1D integral), which isn't generally zero but if you took the volume integral dV=dxdydz (or whatever) over the line you would get zero. Ok, thanks!
Hey everyone,
I am integrating something (specifically 2-forms, but I think this is a general statement) over a set B of (real) codimension 2 in a 4-manifold (CP_2). I've been told that the measure of a set of codimension 2 will vanish, but I don't really understand why. I've been...
Oh no...I think you are right, that's what the Os look like in the paper. I also had a conversation with my advisor about this but it was over e-mail, so I'm sure she wrote O(2) when she really meant (that crazy italic O)(2). Ok, it's back to Hatcher to learn about twisted sheafs! If anyone else...
Hey Everyone,
I'm reading a paper by Claude LeBrun about exotic smoothness on manifolds and he is talking about a connection between polynomials and groups that I am not familiar with (or at least I think that's what he's talking about). He's creating a line bundle (which happens to be...
Great work everyone, I think I'm beginning to get this. I found the chapter in Hatcher on the issue but I'm glad you (Doodle Bob) confirmed what I thought was the relevant result. But I think I understand what's going on, thanks very much everyone!
(and for the record, you guys were more...
Hey everyone,
First of all this is my first post and it's in regards to something I am (supposed to be) learning for my research. The topic is Algebraic Topology, so this was the closest general topic I could find.
The question is in regards to the connection between covering spaces and...