Homotopy Equivalence of Punctured Tori

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!

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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. –  Mariano Suárez-Alvarez May 21 '10 at 0:49
Mariano -- your comment seems to be the best answer. Please consider leaving it as such so as to give the OP the option of accepting it. –  Pete L. Clark May 21 '10 at 11:42

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 :)

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First observe that the fundamental groups of both spaces are isomorphic (both are free groups with 4 generators). Both universal covers are contractible (they are 2 dimensional non compact spaces). Hence both spaces are homotopy equivalent to the classifying space of the free group with 4 generators.

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