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math.AT2026
Stability of persistent path homology of path complexes
Chris Kapulkin, Kyle Koyanagi
The paper proves that the persistent path homology of path complexes is stable under perturbations, and extends this stability to hypergraphs, sequence hypergraphs, and digraphs.
math.AT2026
Discrete homotopy hypothesis for n-types
Daniel Carranza, Chris Kapulkin
We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse…