Homologous to zero but not contractible 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?

This loop bounds a subsurface (torus with one hole) of genus 2 surface. We know that non-trivial elements of first homology group is 'cycles that are not boundary'.
On the other hand since this loop does not bound a disc it is non-trivial on fundemental group.It can be also checked algebraically by drawing planar diagram of genus two surface and see that which element the loop correspond to in fundemental group.
