Basis of linear space (simplices)

Question

Let $M=S^{1}\times S^{1}$ be torus. The projection $\pi : M\longrightarrow S^{1}$ induces $\pi_{*}: C_{k}(M)\longrightarrow C_{k-1}(S^{1})$. if k=1 or k=2, how can we explicit the projection $\pi_{*}?$