562 research outputs found
Barcode Embeddings for Metric Graphs
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.Comment: The newest draft clarifies the proofs in Sections 7 and 8, and
provides improved figures therein. It also includes a results section in the
introductio
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