Barcode embeddings for metric graphs

Steve Oudot; Elchanan Solomon

doi:10.2140/agt.2021.21.1209

Barcode embeddings for metric graphs

Steve Oudot
, Elchanan Solomon

INRIA
Duke University

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly understood. We study a rich homology-based invariant first defined by Dey, Shi and Wang in 2015, which we think of as embedding a metric graph in the barcode space. We prove that this invariant is locally injective on the space of finite metric graphs and globally injective on a generic subset.

Original language	English
Pages (from-to)	1209-1266
Number of pages	58
Journal	Algebraic and Geometric Topology
Volume	21
Issue number	3
DOIs	https://doi.org/10.2140/agt.2021.21.1209
Publication status	Published - 1 Jan 2021
Externally published	Yes

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10.2140/agt.2021.21.1209

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title = "Barcode embeddings for metric graphs",

abstract = "Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly understood. We study a rich homology-based invariant first defined by Dey, Shi and Wang in 2015, which we think of as embedding a metric graph in the barcode space. We prove that this invariant is locally injective on the space of finite metric graphs and globally injective on a generic subset.",

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AB - Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly understood. We study a rich homology-based invariant first defined by Dey, Shi and Wang in 2015, which we think of as embedding a metric graph in the barcode space. We prove that this invariant is locally injective on the space of finite metric graphs and globally injective on a generic subset.

UR - https://www.scopus.com/pages/publications/85113799930

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DO - 10.2140/agt.2021.21.1209

M3 - Article

AN - SCOPUS:85113799930

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JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 3

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Barcode embeddings for metric graphs

Abstract

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