TITLE: Torus removed two points is homotopy equivalent to wedge sum of three circles
QUESTION [5 upvotes]: What is an easy way to see that torus with two points removed is homotopy equivalent to wedge of three circles?
I am trying to see it by viewing the torus as a square with two sides identified, but the intuition isn't clear to me, unlike the case with one point removed.

I am trying to see it as each triangle being retracted to its boundary, but I have no idea how that results in wedge of three circles.
Thanks!

REPLY [2 votes]: You can actually see the three circles in this picture! Look at the three edges incident to the bottom-left corner in your picture. These all become circles after we do the identifications, and they meet at a single point (all four vertices of the rectangle become the same point after identifications). And, after identifications, these three edges are the entire space!