Fundamental theorems of Morse theory on posets
D. Fernández-Ternero, Enrique Macías-Virgós, David Mosquera-Lois, Nicholas A. Scoville, José Antonio Vilches · AIMS Mathematics · 2022
We prove a version of the fundamental theorems of Morse theory in the setting of finite partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the Morse-Pitcher inequalities in that context.