论文标题
Poincar {é}系列和Legendrian结的链接
Poincar{é} series and linking of Legendrian knots
论文作者
论文摘要
在负弯曲的表面上，我们表明，在某些封闭的地球曲线上计数地球弧正交计算正交的poincar {é}序列具有一个持续到整个复杂平面的meromormormorphic延续。当这两种曲线在同源方面都是微不足道的时，我们证明了Poincar {é}系列在0时以链接Legendrian结的数量来解释它的显式有理值。特别是，对于表面上的任何一对点，连接这两个点的所有测量弧的长度决定了其属，对于任何一对杂质琐碎的封闭地球学，所有地理弧的所有地理弧的长度都决定了两种地理位置的长度。
On a negatively curved surface, we show that the Poincar{é} series counting geodesic arcs orthogonal to some pair of closed geodesic curves has a meromorphic continuation to the whole complex plane. When both curves are homologically trivial, we prove that the Poincar{é} series has an explicit rational value at 0 interpreting it in terms of linking number of Legendrian knots. In particular, for any pair of points on the surface, the lengths of all geodesic arcs connecting the two points determine its genus, and, for any pair of homologically trivial closed geodesics, the lengths of all geodesic arcs orthogonal to both geodesics determine the linking number of the two geodesics.
