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A Distance Between Filtered Spaces Via Tripods

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arxiv 1704.03965 v2 pith:6XJ3MAZ2 submitted 2017-04-13 math.AT cs.CG

Facundo Memoli This is my paper · ORCID
classification math.ATcs.CG
keywords spacesfiltrationsstabilitydistancefilteredresultcasecombinatorial
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We present a simplified treatment of stability of filtrations on finite spaces. Interestingly, we can lift the stability result for combinatorial filtrations from [CSEM06] to the case when two filtrations live on different spaces without directly invoking the concept of interleaving. We then prove that this distance is intrinsic by constructing explicit geodesics between any pair of filtered spaces. Finally we use this construction to obtain a strengthening of the stability result.

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Cited by 1 Pith paper

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  1. Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack

    math.MG 2025-07 conditional novelty 6.0 of 10

    Introduces the C-constrained Gromov-Hausdorff distance for chromatic metric pairs and proves that all six diagrams in a six-pack are stable in bottleneck distance with respect to it, up to a factor of 2.

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