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How to compute all homology groups of

$S^1 \times (S^1 \vee S^1)$?

Thank you. I don't see how to define a simplicial structure.

pizet
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  • For some intuition, think of this space as a torus with another torus glued on an 'outer circle' to and 'inner circle' of the first torus. – Dan Rust May 18 '16 at 09:44
  • I am aware of this. And I know the $\Delta$-structure for torus. But how to combine this to get a $\Delta$-structure for my space? – pizet May 18 '16 at 09:47
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    Have you drawn a picture? If it helps, draw it as $[0,1]\times (S^1\vee S^1)$ with the ends identified. A simplicial (or cellular) decomposition should be fairly obvious. – Dan Rust May 18 '16 at 09:54
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    just use cellular decomposition instead simplicial one – Andrey Ryabichev May 18 '16 at 13:24

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