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I am studying some concepts of algebraic topology myself, and I read lately a bit about cohomology rings (created by the direct sum of cohomology groups) but besides all definitions I could not find any information.

  • What are they good for?
  • How do we use them?
  • Could someone give me a very short descriptive example?

Thank you

  • 0
    The example on the wiki page for cup product will be helpful: http://en.wikipedia.org/wiki/Cup_product2011-05-17
  • 3
    to add to the excellent answers below - a couple of classic cases where the (co)homology and fundamental groups coincide, yet the spaces are not isomorphic: (1) $S^2 \vee S^1 \vee S^1$ and $S^1 \times S^1$, and (2) $S^1 \vee S^2 \vee S^3$ and $S^1 \times S^2$. (2) is a bit harder to show (at least it was for me yesterday)2011-05-18

3 Answers 3