平面曲线的中间连杆
Intermediate links of plane curves
摘要：
对于光滑复曲线C，我们考虑C与B（r）的边界的连线L（r）交，其中B（r）表示半径r>0的欧氏球。证明了由L（r）作复球极平面投影得到的图D（r）满足B（r）中C部分的欧拉示性数等于D（r）的旋转数减去D（r）的扭曲。结果表明，如果D（r）不存在负的Seifert圈，且L（r）是强拟正的，则Yamada-Vogel算法应用于D（r）得到一个拟正辫子.
英文摘要：
For a smooth complex curve C, we consider the link L(r) intersection of C with the boundary of B(r), where B(r) denotes an Euclidean ball of radius r>0. We prove that the diagram D(r) obtained from L(r) by a complex stereographic projection satisfies that the Euler characteristic of the part of C in B(r) equals the rotation number of D(r) minus the writhe of D(r). As a consequence we show that if D(r) has no negative Seifert circles and L(r) is strongly quasipositive and fibred, then the Yamada-Vogel algorithm applied to D(r) yields a quasipositive braid.
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