Morse-Bott inequalities for endomorphisms

Abstract

Let $K$ be a finite simplicial complex, let $g:K\to K$ be a simplicial map and let $f$ be a discrete Morse-Bott function on $K$ satisfying $f(g(\ddot{I}ƒ))\le f(\ddot{I}ƒ)$ for all simplices $\ddot{I}ƒ$ 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 $f$.

Hybrid approach combining Lefschetz fixed point theory and Morse-Bott theory. Comments are welcome