Euler characteristic and Lipschitz-Killing curvatures of closed semi-algebraic sets
Nicolas Dutertre (LATP)
TL;DR
This paper establishes a formula linking the Euler-Poincaré characteristic of closed semi-algebraic sets to their Lipschitz-Killing curvatures, providing a new geometric insight.
Contribution
It introduces a novel formula connecting topological and geometric invariants of semi-algebraic sets.
Findings
Derived a formula relating Euler characteristic and Lipschitz-Killing curvatures
Bridged topological and geometric properties of semi-algebraic sets
Enhanced understanding of curvature invariants in algebraic geometry
Abstract
We prove a formula that relates the Euler-Poincar\'e characteristic of a closed semi-algebraic set to its Lipschitz-Killing curvatures
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