论文标题
未标记的简单长度光谱刚度
Unmarked simple length spectral rigidity for covers
论文作者
论文摘要
我们证明，每个封闭的封闭式欧拉特征的可定向表面都承认，一对有限度的覆盖层在s上长度是等的，但通常不是简单的等速长度，而在S上则是同一镜头。为此，我们首先是当两个有限度的覆盖范围在一个连接的，可定向的负欧拉特特征表面的有限度覆盖率上，而euler特征的等级是简单的等级。我们还使用相同的完整未标记的长度光谱构造双曲线表面X和Y，因此，对于每个K，与曲线相关的长度集合与大多数K自身交流相关。
We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simple length isospectral over S. To do this, we first characterize when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations. We also construct hyperbolic surfaces X and Y with the same full unmarked length spectrum but so that for each k, the sets of lengths associated to curves with at most k self-intersections differ.
