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.
Citation
Steve Oudot. Elchanan Solomon. "Barcode embeddings for metric graphs." Algebr. Geom. Topol. 21 (3) 1209 - 1266, 2021. https://doi.org/10.2140/agt.2021.21.1209
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