Repeat Exercise 11, but view the map f as a map of the torus X into itself, inducing maps f_*n : H_n(X) → H_n(X).

Data from Exercises 11

With reference to Exercise 10, the torus X can be mapped onto its circle b (which is homeomorphic to S¹) by a variety of maps. For each such map f : X → b given below, describe the homomorphism f_*n : H_n(X) → H_n(b) for n = 0, 1, and 2, by describing the image of generators of H_n(X) as in Exercise 10.