Every closed geodesic $\gamma$ on a surface has a canonically associated knot $\widehat{\gamma }$ in the projective unit tangent bundle. We study, for $\gamma$ filling, the volume of the associated knot complement with respect to its unique complete hyperbolic metric. We provide a lower bound for the volume relative to the number of homotopy classes of $\gamma$‐arcs in each pair of pants of a pants decomposition of the surface. This paper relies extensively on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.

中文翻译：

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周期性测地线补数的下限

每个封闭测地线 $\gamma$ 在表面上具有规范关联的结 $\widehat{\gamma }$在投影单位切线束中。我们学习$\gamma$填充时，相关联的结的体积相对于其唯一完整的双曲度量而言。我们提供了相对于同构类的数量的下界$\gamma$在每条裤子的弧形内裤的表面分解。本文广泛依赖于彩色图形。对颜色的某些引用在印刷版本中可能没有意义，我们请读者阅读包含颜色数字的在线版本。