测地线和压缩体
Geodesics and compression bodies
摘要：
考虑压缩体C上亏格为2的正边界和亏格为1的负边界的双曲结构。请注意，C形变收缩核到圆环边界和端点位于圆环上的单个圆弧的并集。我们称之为C的核心隧道。我们猜想，在C上的任何几何有限结构中，核心隧道是测地线的同位素。通过考虑福特域，我们证明了这一猜想适用于许多几何有限结构。此外，我们给出了一个算法来计算福特域这样的流形，并已实现可视化这些福特域的程序。我们的计算机实现提供了进一步的证据的猜想。
英文摘要：
We consider hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. Note that C deformation retracts to the union of the torus boundary and a single arc with its endpoints on the torus. We call this arc the core tunnel of C. We conjecture that, in any geometrically finite structure on C, the core tunnel is isotopic to a geodesic. By considering Ford domains, we show this conjecture holds for many geometrically finite structures. Additionally, we give an algorithm to compute the Ford domain of such a manifold, and a procedure which has been implemented to visualize many of these Ford domains. Our computer implementation gives further evidence for the conjecture.
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