We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pairwise cross at most $k$ times.

翻译：我们证明了可定向曲面上绘制的多重图交叉引理的一个推广，其中假设每对边由非同伦的简单弧绘制，且这些弧两两相交至多$k$次。