>>11536586You can construct it via CW complex with
1 2-cell, 0 1-cells, 1 0-cell
or
2 2-cells, 1 1-cells, 1 0-cell
or in many other way
You'll notice that the Euler characteristic doesn't change : #2-cells - #1-cells + #0-cells =2
This is because homology is a homotopy invariant. Cellular chain groups are generated freely by the n-cells, and the alternating sum of ranks doesn't change as you pass to homology, hence is a homotopy (and, a fortiori, topological) invariant.
