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 $X/B$?]

Figure 1
The space(s) mentioned above

Proof.

$\square$