For the simplicial complex X and subcomplex a of Exercise 8, form the exact homology sequence of

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For the simplicial complex X and subcomplex a of Exercise 8, form the exact homology sequence of the pair (X, a) and verify by direct computation that this sequence is exact.


Data from Exercises 8

Repeat Exercise 6 with X the Klein bottle of Fig. 43.2 and Fig. 43.4. 


Figure 43.2

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