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Two smooth oriented finite curves g1, g2$g_1, g_2$ on e.g. the 2-dimensional torus can intersect each other transversally in two ways: either the pair (Tg1(x),Tg2(x))$(Tg_1(x),Tg_2(x))$ of tangent vectors in the intersection point x$x$ is a positively oriented, or a negatively oriented basis. n(x)=1$n(x)=1$ if the former is the case and n(x)=-1$n(x)=-1$ otherwise.

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

Two smooth oriented finite curves g1, g2 on e.g. the 2-dimensional torus can intersect each other transversally in two ways: either the pair (Tg1(x),Tg2(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?

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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Term for number of crossings of smooth curves

Two smooth oriented finite curves g1, g2 on e.g. the 2-dimensional torus can intersect each other transversally in two ways: either the pair (Tg1(x),Tg2(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?