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What is the homology groups of the torus with a sphere inside?
Posted:
Jan 24, 2013 3:56 PM


I'm trying to find the homology groups of this space X in this link below:
http://tinypic.com/r/bymmd/6
The easiest part is H_0(X)=Z, because X is connected. In order to find H_1(X) I think the easiest method is finding its fundamental group, but I don't know the fundamental group of this space, it's my first problem.
My second problem is to find H_2(X), I don't know how to triangulate this picture and I don't know how to use MayerVietoris in this case.
I really need help here, any help or comment would be appreciated.
Thanks a lot



