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.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: JP17H06462
Funding statement: This work is supported by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number JP17H06462.
Acknowledgements
I would like to thank Yasuhide Numata and Masahiko Yoshinaga for discussions. I would also like to thank Yuzhou Gu for pointing out a mistake in an earlier version of this paper.
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