Hatcher 2.1.17

Hatcher, Algebraic Topology, Chapter 2, Section 1

17. (a) Compute the homology groups H_n(X,A) when X=S^2 or X=S^1\times S^1 and A is a finite set of points in X. (b) Compute the groups H_n(X,A) and H_n(X,B) for X a closed orientable surface of genus two with A and B the circles shown in Figure 1 below. [What are X/A and X/B?]

Hatcher 2.1.17
Figure 1
The space(s) mentioned above

Proof.

\square

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