Isospectral surfaces with distinct covering spectra via Cayley graphs
Isospectral surfaces with distinct covering spectra via Cayley graphs
复制标题
通过凯莱图具有不同覆盖光谱的等谱表面
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Craig J. Sutton
中科院分区：
文献类型：
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作者：
B. Smit;Ruth Gornet;Craig J. Sutton
覆盖谱是黎曼流形的几何不变量，更一般地说是度量空间的几何不变量，它通过隔离一部分长度谱来测量其一维洞的大小。在以前的文件中，我们证明了覆盖谱是不是一个频谱不变量的流形在三维和更高。在这篇文章中，我们给出了一个例子，两个等谱凯莱图，承认长度空间结构不同的覆盖谱。由此，我们推导出存在无限多对的Sunada等谱曲面不等覆盖谱。
The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we demonstrated that the covering spectrum is not a spectral invariant of a manifold in dimensions three and higher. In this article we give an example of two isospectral Cayley graphs that admit length space structures with distinct covering spectra. From this we deduce the existence of infinitely many pairs of Sunada-isospectral surfaces with unequal covering spectra.