Morse-Bott inequalities for endomorphisms

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Enrique Macías-Virgós, Alejandro O. Majadas-Moure, David Mosquera-Lois, José Antonio Vilches
Cited by: 0

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 $f(g(σ))\leq f(σ)$ for all simplices $σ$ 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 $f$.

Fields of Study & Subjects

Geometric and Algebraic Topology Topological and Geometric Data Analysis Homotopy and Cohomology in Algebraic Topology

Publication details

Journal / source
arXiv (Cornell University)
Publication date
2 February 2026
Document type
Preprint