Abstract We introduce an intrinsic filtration to the magnitude chain complex of a metric space, and study basic properties of the associated spectral sequence of the magnitude homology. As an application, the third magnitude homology of the circle is computed.

中文翻译：

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量级复数的平滑过滤

摘要 我们对度量空间的幅度链复数引入了内在过滤，并研究了幅度同源性的相关谱序列的基本性质。作为一个应用，计算了圆的第三级同源性。