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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.…
math.AT2024
Morse theory for chromatic Delaunay triangulations
Abhinav Natarajan, Thomas Chaplin, Adam Brown +1
The chromatic alpha filtration is a generalization of the alpha filtration that can encode spatial relationships among classes of labelled point cloud data, and has applications in…