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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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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