Consider the map f of the Klein bottle in Fig. 43.2 given by mapping a point Q of the rectangle in Fig. 43.2 onto the point of b directly opposite ( closest to) it. Note that b is topologically a I-sphere. Compute the induced maps f_*n : H_n(X) → H_n(b) for n = 0, 1, and 2, by describing images of generators of H_n(X).

Figure 43.2

Transcribed Image Text:

P b. P a a P b P