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math.AT2026
The poset of cancellations induced by gradient dynamics in a filtered Lefschetz complex
Herbert Edelsbrunner, MichaÅ LipiÅski, Marian Mrozek +1
Motivated by questions about simplification of topology, we take a discrete approach to the dependency of simplifying operations, using methods based on combinatorial gradient dyna…
math.AT2025
The Depth Poset under Transpositions in the Filter
Herbert Edelsbrunner, MichaÅ LipiÅski, Marian Mrozek +2
The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing…