Looking for instructive examples on the difference between homology and homotopy, I found here the following example:
Example: Consider an oriented loop separating a genus $2$ surface into two genus $1$ punctured surfaces. This loop is nontrivial in the fundamental group, but is trivial in homology, i.e. it is homologous to zero.
I don't understand this. I'm imagining a double torus with a rubber band around the "connection of the two tori", but this curve is contractible since I can just pull the rubber band off around either hole. What is meant in the example?