Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Reading the "Differential Topology" of V.Guillemin and A.Pollack, i found a definition of the Euler Characteristic different from the other one using the simplicial complex and betti number (ex. for surface $\chi(S) = F- L +V$). That definition said that $\chi(S) = I(\Delta,\Delta)$ where $\Delta$ is the diagonal of $S\times S$, the self-intersection number of $\Delta$. I know that there is a proof of that definition using the differential forms and the property of cohomolgy group, but i ask if there is another proof not using that, using only basic knowledge of differential topology (like in the Guillemin's book). Thanks for any response.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.