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math.AT2026
The fiber of multiparameter persistent homology for simplicial complexes
Heather A. Harrington, Ulrike Tillmann, Maria Torras-Pérez
Vector-valued functions on finite simplicial complexes give rise to multiparameter sublevel set filtrations and corresponding persistent homology. We study the associated inverse p…
math.AT2024
A notion of homotopy for directed graphs and their flag complexes
Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
Directed graphs can be studied by their associated directed flag complex. The homology of this complex has been successful in applications as a topological invariant for digraphs.…