Smoothness filtration of the magnitude complex
Kiyonori Gomi
TL;DR
This paper introduces a new intrinsic filtration for the magnitude chain complex of metric spaces, analyzes its spectral sequence, and computes the third magnitude homology of the circle, advancing understanding of magnitude homology.
Contribution
It presents a novel intrinsic filtration for the magnitude chain complex and explores its spectral sequence, including explicit computations for the circle.
Findings
Spectral sequence of the new filtration analyzed
Third magnitude homology of the circle computed
Provides insights into the structure of magnitude homology
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Geometric and Algebraic Topology