Source Title:
Forum Mathematicum
|
Volume/Issue:
Volume 32: Issue 3

Smoothness filtration of the magnitude complex

Kiyonori Gomi 1
  • 1 Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, Japan
Kiyonori Gomi
  • Corresponding author
  • Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan
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DOI:
https://doi.org/10.1515/forum-2019-0091
|
Published online:
17 Jan 2020

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.

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    N. Otter, Magnitude meets persistence. Homology theories for filtered simplicial sets, preprint (2018), https://arxiv.org/abs/1807.01540.

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Article information

Received:
2019-04-08
Revised:
2019-09-23
Published Online:
2020-01-17
Published in Print:
2020-05-01

Funding Source:
Japan Society for the Promotion of Science
Award identifier / Grant number:
JP17H06462

This work is supported by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number JP17H06462.

Citation Information: 
Forum Mathematicum, Volume 32, Issue 3, Pages 625–639, eISSN 1435-5337, ISSN 0933-7741, DOI: https://doi.org/10.1515/forum-2019-0091.

© 2020 Walter de Gruyter GmbH, Berlin/Boston.

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Journal + Issues

Forum Mathematicum

Online ISSN:
1435-5337
First published:
01 Jan 1989
Language:
English
Publisher:
De Gruyter

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