Isometry Theorem for Continuous Quiver of Type $\tilde{A}$

Minghui Zhao; Xiaowen Gao

Isometry Theorem for Continuous Quiver of Type $\tilde{A}$

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arxiv 2412.12462 v2 pith:HS3QGK6M submitted 2024-12-17 math.RT

Xiaowen Gao , Minghui Zhao This is my paper · ORCID

classification math.RT

keywords continuousisometryquivertheoremtypetildegeneralizehomology

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abstract

The Isometry Theorem for continuous quiver of type $A$ plays an important role in persistent homology. In this paper, we shall generalize Isometry Theorem to continuous quiver of type $\tilde{A}$.

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An isometry theorem for persistent homology of circle-valued functions
math.AT 2025-06 conditional novelty 7.0 of 10

For persistence modules of circle-valued functions, the interleaving distance equals the bottleneck distance between arc barcodes on a geometric model.

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