15 citations · 24 across the 9 of their papers we have counts for
4 papers · 1 filter
The fiber of persistent homology for trees
David Beers, Jacob Leygonie
Consider the space of continuous functions on a geometric tree whose persistent homology gives rise to a finite generic barcode . We show that there are exactly as many path…
Fiber of Persistent Homology on Morse functions
Jacob Leygonie, David Beers
Let be a Morse function on a smooth compact manifold with boundary. The path component containing of the space of Morse functions giving rise to…
The Fiber of Persistent Homology for simplicial complexes
Jacob Leygonie, Ulrike Tillmann
We study the inverse problem for persistent homology: For a fixed simplicial complex , we analyse the fiber of the continuous map on the space of filters that assi…
A Framework for Differential Calculus on Persistence Barcodes
Jacob Leygonie, Steve Oudot, Ulrike Tillmann
We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to…