Volume 21, issue 3 (2021)

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Barcode embeddings for metric graphs

Steve Oudot and Elchanan Solomon

Algebraic & Geometric Topology 21 (2021) 1209–1266

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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inverse problems, applied topology, metric graphs, persistent homology
Mathematical Subject Classification 2010
Primary: 18G60, 55U10, 57M15, 57M50
Received: 19 July 2018
Revised: 4 May 2020
Accepted: 11 June 2020
Published: 11 August 2021
Steve Oudot
INRIA Saclay
Elchanan Solomon
Duke University
Durham, NC
United States