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I've found this table of homology groups of the tori $T^n$.

My question is: How did they compute these? More generally: what's the "recipe" to compute the homology group of say, a cell complex?

Many thanks for your help!

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    You might want to look at Allen Hatcher's book "Algebraic Topology," which is available at his webpage for free download.2011-05-25
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    I'm actually reading that but not sequentially. I did have a look but couldn't find where he does it. Can someone point me to it please?2011-05-25
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    The section on cellular homology, starting p137 is relevant. In particular example 2.36 on p141 does the computation for surfaces of genus g, including the torus as a special case.2011-05-25
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    You can use the Kunneth formula: http://en.wikipedia.org/wiki/K%C3%BCnneth_theorem2011-05-25
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    I think I have to look into "Cellular homology".2011-05-25

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