双曲复线列无穷远点的纤维杆和非纤维杆
Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements
摘要：
设F是R或C，d是F在R上的维数.用P（F）表示仿射平面A（F）或F上的双曲平面H（F）。P（F）中k条直线的排列L（双曲情形中为两两不平行）在无穷远处有一个链环K（L），它包括在（2d-1）-球面中的k个不打结的（d-1）-球面，其拓扑反映了L“在无穷远处”的组合学。仿射F-线列无穷远点处的链环类适当地包含在双曲F-线列无穷远点处的链环类中。许多链接在无穷远的（基本上非仿射）连接双曲C线安排是远远没有纤维化;证明是一个直接建设，使用“勒让德铭文”。相反，如果（仿射或双曲）R-线排列L是连通的，那么它的复化（仿射或双曲C-线排列）在无穷远处有一个纤维链;证明使用A 'Campo除法。
英文摘要：
Let F be R or C, d the dimension of F over R. Denote by P(F) either the affine plane A(F) or the hyperbolic plane H(F) over F. An arrangement L of k lines in P(F) (pairwise non-parallel in the hyperbolic case) has a link at infinity K(L) comprising k unknotted (d-1)-spheres in the (2d-1)-sphere, whose topology reflects the combinatorics of L `at infinity'. The class of links at infinity of affine F-line arrangements is properly included in the class of links at infinity of hyperbolic F-line arrangements. Many links at infinity of (essentially non-affine) connected hyperbolic C-line arrangements are far from being fibered; the proof is a direct construction, using ``Legendrian inscription''. In contrast, if the (affine or hyperbolic) R-line arrangement L is connected, then its complexification (an affine or hyperbolic C-line arrangement) has a fibered link at infinity; the proof uses A'Campo's divides.
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