I was told recently that if I take a 2-torus (genus 2) and remove 1 point, then this is homotopy equivalent to a torus with 3 points removed. This may be really easy but I don't see it.


Thank you!



Homotopy Equivalence of Punctured Tori
A surface minus a finite number of points is homotopy equivalent to a bouquet of circles, and two bouquets of circles are homotopy equivalent iff they have the same number of circles.


This two observations and a little picture to see how many circles are involved in your example should do it :)


