What question did this study set out to answer?

The aim is to establish inequalities that relate the dynamics of simplicial maps and discrete Morse–Bott functions.

April 13, 2026Open Access

Morse–Bott inequalities for endomorphisms

Key Points

The aim is to establish inequalities that relate the dynamics of simplicial maps and discrete Morse–Bott functions.
Defined a simplicial complex K and a simplicial map g: K → K.
Invested discrete Morse–Bott functions under a specific condition involving g and simplices σ.
Established a set of inequalities generalizing known Morse–Bott inequalities.
Showed that the inequalities hold for all simplices σ in K.
Recovered classical Morse–Bott inequalities for the case where g is the identity.

Abstract

Abstract Let K be a finite simplicial complex, let g: K K g: K → K be a simplicial map and let f be a discrete Morse–Bott function on K satisfying f (g () ) f () f (g (σ) ) ≤ 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.

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Cite This Study

Macías-Virgós et al. (Sat,) studied this question.

synapsesocial.com/papers/69dc88583afacbeac03ea310 https://doi.org/https://doi.org/10.1007/s13398-026-01858-w

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