Discrete Morse theory for the barycentric subdivision

Abstract

Let $F$ be a discrete Morse function on a simplicial complex $L$. We construct a discrete Morse function $\Delta (F)$ on the barycentric subdivision $\Delta (L)$. The constructed function $\Delta (F)$ "behaves the same way" as $F$, i. e. has the same number of critical simplexes and the same gradient path structure.

11 pages 3 figures