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Math Help - Fundamental Group of Plane Minus Two Points

  1. #1
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    Fundamental Group of Plane Minus Two Points

    Need help with the following:

    Calculate the fundamental group of the plane minus the points (0,1) and (0,-1).

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by DJDorianGray View Post
    Need help with the following:

    Calculate the fundamental group of the plane minus the points (0,1) and (0,-1).

    Thanks in advance!

    An idea: draw two circles with radius 1 and center (0,-1),(0,1) resp. around the two given points, and now "shrink" the exterior of both circles to the point (0,0) and ALSO the interior of both circles shrink to the same point (0,0) ==> you get the plane minus those two points is homotopically equivalent to a bouquet of two circles (i.e., the figure \infty), and it is well known, and as far as I remember not hard at all, to prove that this bouquet's fund. group is the free group in 2 generators.

    Tonio
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