We can form the topological real projective plane X, using Fig. 43.14, by joining the semicircles a

Question:

We can form the topological real projective plane X, using Fig. 43.14, by joining the semicircles a so that diametrically opposite points come together and the directions of the arrows match up. This cannot be done in Euclidean 3-space R³. One must go to R⁴ Triangulate this space X, starting with the form exhibited in Fig. 43.14, and compute its homology groups.

Figure 43.14