CW complex for infinite holed torus? (Surface of infinite genus)

  • #1
125
0

Main Question or Discussion Point

I am just trying to figure out how to make a CW complex for this. For the n-genus orientable manifold (connect sum of n-tori) I feel like a lot of things make sense, fundamental group, CW complex, etc. But in the infinite case, things seem to fall apart. For example, I can not figure out how the fundamental group is a free group. I was hoping to figure this out by first looking at the CW complex of this surface, but I'm not sure I can picture it.


IN a finite case, I just have a single 0 cell (1 vertex), 2n 1-cells, and a single 2 cell. BUt does this hold at the infinite case? If not what's an alternate way to visualize it?
 

Answers and Replies

  • #2
13,253
10,217
I would consider projective limits here, although I'm not sure this would help. To precisely determine where and why "things fall apart" would also be of great help.
 

Related Threads on CW complex for infinite holed torus? (Surface of infinite genus)

Replies
7
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
3
Views
2K
Replies
1
Views
4K
Replies
27
Views
719
Replies
1
Views
1K
Top