Euler Characteristics and Homotopy Types of Definable Sublevel Sets, with Applications to Topological Data Analysis

Mattie Ji, Kun Meng

Given a definable function $f:S\to \mathbb{R}$ on a definable set $S$, we study sublevel sets of the form $S_t^f:=\{x\in S:f(x)\le t\}$ for all $t\in \mathbb{R}$. U…