- #1
saminator910
- 96
- 1
On all manifolds dimension 1-3, there is only one differential structure per manifold, yet in higher dimensions it seems to follow no pattern. Is there a physical reason why you can construct a certain number on any given dimension? Also, what is it about dimension 4 that is so strange? Using surgery, one can construct an infinite number of differential structures on a 4 manifold, and of course most know of the Poincare conjecture. What is it that separates 4 from all the others in this way?