胡伯定理的一个拓扑版本
A topological version of Huber's theorem
AI总结：
针对闭双曲曲面X，证明长度不超过L的本原闭测地线拓扑类型数目渐近于\\(\frac{1}{|\Isom(X)|}\frac{e^L}{2L}\\)，使胡伯渐近式经拓扑类型取商后仍成立，仅差有限对称因子。
AI中文摘要：
设X为闭双曲曲面，我们证明长度不超过L的本原闭测地线的拓扑类型数目渐近于\\(\frac{1}{|\Isom(X)|}\frac{e^L}{2L}\\)（L增大时）。因此，胡伯渐近式在按拓扑类型取商后仍保持不变，仅相差来自X的等距群的有限对称因子。
英文摘要：
Let $X$ be a closed hyperbolic surface. We prove that the number of topological types of primitive closed geodesics of length at most $L$ is asymptotic to \[ \frac{1}{|\Isom(X)|}\frac{e^L}{2L}. \] as $L$ grows. Thus Huber's asymptotic remains unchanged after quotienting by topological type, up to the finite symmetry factor coming from the isometry group of $X$.
