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Homology of RP(2)

  1. Dec 25, 2007 #1
    I'm currently learning some homology theory but I have some difficulties computing homology groups of a few simple spaces. If someone could do the explicit calculation for RP(2), it would be really nice.

    Thank you :)
     
  2. jcsd
  3. Dec 25, 2007 #2

    mathwonk

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    the universal covering space is the 2 sphere, so pi 1 is Z/2Z, hence also the first homology group. that does it since the space is connected non orientable manifold so the zeroth homology is Z and the second homology i guess is zero.

    i am just recalling this from 40 years ago since they don't let me teach topology for some reason, so i could be wrong.
     
  4. Dec 25, 2007 #3

    mathwonk

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    another approach is to represent RP^2 as a circle with a disc attached by a map of degree 2. then there is a little formula for the homology groups, in the chapter on cell complexes.
     
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