I seem to have wrong understanding of CW complex and it would be nice if someone could help me out.
The definition I have for Cell complex is the usual one I think. We define glueing of cells and hence define a cell complex and so forth.
Now an easy example I want to consider is a 2-disc. Homology group of 2-disc is clearly same as homology group of a point and hence 0th homology group is $\mathbb{Z}$ and every group is 0. But other way of looking at it (which I'm sure I'm wrong) is that 2-disc is simply a one 2-cell and hence we can calculate the homology group of it to get $\mathbb{Z}$ for 2nd homology group and 0 for all others.
So why is a 2-disk not a simply 2-cell? It seem to make sense to me but clearly it's wrong.