A cycle $A$ homologous to another cycle $B$ is well disjoint with $B$?

Question

On Griffiths and Harris p.49, it says: Consider a standard torus $T$ and two $1$-cycles $A$ and $A'$, ... while a cycle homologous to $A$, for example $A'$, may be well disjoint from $A$.

I feel confused, because if $A,A'$ are homologous then $A-A'$ is a boundary of a $2$-chain, so $A,A'$ have to be connected (since the boundary of $\Delta^2$ is connected), then it's a contradiction from Griffiths and Harris. Where did I miss?

Answer 1

Here is some intuition, which can be formalized depending on what homology theory you are using specifically. Think of the following blue $1$ cycles, and think of the boundary of the pink $2$ cycle.