Work

The fiber of persistent homology for trees

Year: 2025

Type: article

Abstract: Consider the space of continuous functions on a geometric tree X whose persistent homology gives rise to a finite generic barcode D. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is D. We find that each component is homotopy equivalent to a configuration space on X with specialised constraints encoded by the merge tree. For barcodes D with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.

Source: Journal of Applied and Computational Topology

DOI: 10.1007/s41468-025-00213-z

Authors: David Beers, Jacob Leygonie

Institution: University of Oxford

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: London Mathematical Society, Engineering and Physical Sciences Research Council, Mathematical Institute, University of Oxford