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
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar


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.

  • [1]

    R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Grad. Texts in Math. 82, Springer, New York, 1982.

  • [2]

    K. Gomi, Magnitude homology of geodesic space, preprint (2019),

  • [3]

    R. Hepworth, Magnitude cohomology, preprint (2018),

  • [4]

    R. Hepworth and S. Willerton, Categorifying the magnitude of a graph, Homology Homotopy Appl. 19 (2017), no. 2, 31–60.

    • Crossref
    • Export Citation
  • [5]

    B. Jubin, On the magnitude homology of metric spaces, preprint (2018),

  • [6]

    R. Kaneta and M. Yoshinaga, Magnitude homology of metric spaces and order complexes, preprint (2018),

  • [7]

    A. Kono and D. Tamaki, Generalized Cohomology, Transl. Math. Monogr. 230, American Mathematical Society, Providence, 2006.

  • [8]

    T. Leinster, The magnitude of metric spaces, Doc. Math. 18 (2013), 857–905.

  • [9]

    T. Leinster and M. Shulman, Magnitude homology of enriched categories and metric spaces, preprint (2017),

  • [10]

    M. W. Meckes, Positive definite metric spaces, Positivity 17 (2013), no. 3, 733–757.

    • Crossref
    • Export Citation
  • [11]

    N. Otter, Magnitude meets persistence. Homology theories for filtered simplicial sets, preprint (2018),

  • [12]

    E. H. Spanier, Algebraic topology, Springer, New York, 1981.

Purchase article
Get instant unlimited access to the article.
Log in
Already have access? Please log in.

Log in with your institution

Journal + Issues

Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.