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2022•AIMS MathematicsOpen access

Fundamental theorems of Morse theory on posets

D. Fernández-Ternero, Enrique Macías-Virgós, D. Mosquera-Lois, Nicholas A. Scoville, José Antonio Vilches

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Discrete Morse theory, Morse code, Morse theory, Mathematics, Context (archaeology), Circle-valued Morse theory, Pure mathematics, Discrete mathematics

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