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arXiv · 2602.02075

Morse-Bott inequalities for endomorphisms

Enrique Macías-Virgós·Alejandro O. Majadas-Moure·David Mosquera-Lois·José Antonio Vilches
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Abstract

Let $K$ be a finite simplicial complex, let $g\colon K\to K$ be a simplicial map and let $f$ be a discrete Morse-Bott function on $K$ satisfying $f(g(\sigma))\leq f(\sigma)$ for all simplices $\sigma$ in $K$. We establish a set of inequalities (generalizing the Morse-Bott inequalities which we recover as a particular case when $g$ is the identity) relating the dynamics of $g$ and $f$.

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Enrique Macías-Virgós, Alejandro O. Majadas-Moure, David Mosquera-Lois, José Antonio Vilches. 2026-02-02. Morse-Bott inequalities for endomorphisms. https://arxiv.org/abs/2602.02075

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