The connected sum of two surfaces $S_1$ and $S_2$ is formed by removing a circular hole from each surface and identifying the boundaries together
Show that the connected sum $S_1$ # $S_2$ is commutative and associative
It seems reasonable that, up to homeomorphism:
- $S_1$ # $S_2=S_2$ # $S_1$
- ($S_1$ # $S_2$)#$S_3$ = $S_1$ # ($S_2$#$S_3$)
How could I show this explicitly?