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arXiv · 1712.03630

Barcode Embeddings for Metric Graphs

Steve Oudot·Elchanan Solomon
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Abstract

Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly-understood. In this paper we study a rich homology-based invariant first defined by Dey, Shi, and Wang, 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 metric graphs and globally injective on a GH-dense subset. Moreover, we show that is globally injective on a full measure subset of metric graphs, in the appropriate sense.

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Steve Oudot, Elchanan Solomon. 2017-12-11. Barcode Embeddings for Metric Graphs. https://doi.org/10.2140/agt.2021.21.1209

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