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Two smooth oriented finite curves $g_1, g_2$ on e.g. the 2-dimensional torus can intersect each other transversally in two ways: either the pair $(Tg_1(x),Tg_2(x))$ of tangent vectors in the intersection point $x$ is a positively oriented, or a negatively oriented basis. $n(x)=1$ if the former is the case and $n(x)=-1$ otherwise.

Is there a name for the integer obtained when we take the sum of $n(x)$ over all intersection points $x$?

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    $\begingroup$ It's usually called the algebraic intersection of the two curves. $\endgroup$
    – Tony Huynh
    Commented Dec 12, 2011 at 13:37
  • $\begingroup$ @Tony has given the answer, but I want to know what "finite curves" are... $\endgroup$
    – Igor Rivin
    Commented Dec 12, 2011 at 13:44

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To remove this question from the "unanswered" queue: As Tony Huynh said in a comment, the sum of $n(x)$ is called the algebraic intersection of the curves.

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