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Magnitude homology of geodesic space

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arxiv 1902.07044 v3 pith:RGFZQ667 submitted 2019-02-19 math.AT

Magnitude homology of geodesic space

Kiyonori Gomi This is my paper
classification math.AT
keywords homologymagnitudemetricspacedescriptiongeodesicgroupssimplicial
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This paper studies the magnitude homology groups of geodesic metric spaces. We start with a description of the second magnitude homology of a general metric space in terms of the zeroth homology groups of certain simplicial complexes. Then, on a geodesic metric space, we interpret the description by means of geodesics. The third magnitude homology of a geodesic metric space also admits a description in terms of a simplicial complex. Under an assumption on a metric space, the simplicial description allows us to introduce an invariant of third magnitude homology classes as an intersection number. Finally, we provide a complete description of all the magnitude homology groups of a geodesic metric space which fulfils a certain non-branching assumption.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Filtered Varchenko–Gelfand algebras are invariant under a Cremona coefficient swap for two-coordinate arrangements, producing a counterexample to the Yagi–Yoshinaga tope-graph conjecture.

  2. Homotopy theories via the magnitude-path spectral sequence

    math.AT 2026-06 unverdicted novelty 7.0

    Defines r-quasi-isomorphisms and r-cofibrations on generalized metric spaces so that each page of the magnitude-path spectral sequence satisfies metric Eilenberg-Steenrod axioms and supports Brown category structures ...

  3. A Centrality Measure Using Magnitude Homology

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    A new family of graph centrality measures based on the change in (Eulerian) magnitude homology after deleting a vertex, with a proven locality property.

  4. Orlik--Solomon sheaf homology of geometric lattices

    math.CO 2026-07 accept novelty 6.0

    Orlik–Solomon sheaf homology on a geometric lattice concentrates in top degree and decomposes as a sum of local OS algebras tensored with top homology of complementary geometric semilattices.

  5. Magnitude of metric measure spaces and integrals over geodesics

    math.DG 2026-05 unverdicted novelty 6.0

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