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I am trying to compute the fundamental group pair of pants, so that figure is homotopy equivalent to a disk with two sub-disks removed as shown in the picture. How can I compute the fundmental group of a disk with two smaller sub-disks removed ?enter image description here

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    the answer is the free group of rank two because this space is homotopically equivalent to the figure eight curve – 2017-02-15
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    This in turn is homotopic to a figure eight – 2017-02-15
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    The next step ist to reduce the problem by finding yet another homotopy equivalence. Try to move the two holes to the center of the disk and shrink the disk to the holes. What do you get? – 2017-02-15
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    Yeah right it is homotopy equivalent to figure eight which is free group of rank 2 – 2017-02-15
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    @janmarqz why do you answer it directly? OP put alot of work in hist first step and now you give him the answer without letting him try? – 2017-02-15
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    @noctusraid: the OP should know where he is going and what he will find – 2017-02-15
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    Seifert van Kampen? – 2017-02-15

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