Virtual Poincar\'e polynomial of the link of a real algebraic variety

TL;DR

This paper introduces the virtual Poincaré polynomial as a new, stronger topological invariant for the link of a real algebraic variety, extending beyond the traditional Euler characteristic.

Contribution

The paper proves that the virtual Poincaré polynomial is well-defined for the link of a real algebraic variety, providing a novel invariant for topological analysis.

Findings

Virtual Poincaré polynomial is well-defined for the link

Stronger invariant than Euler characteristic

Enhances understanding of local topological properties

Abstract

The Euler characteristic of the link of a real algebraic variety is an interesting topological invariant in order to discuss local topological properties. We prove in the paper that an invariant stronger than the Euler Characteristic is well defined for the link of an algebraic variety: its virtual Poincar\'e polynomial.