Virtual Poincaré polynomial of the link of a real algebraic variety

The link of an affine real algebraic variety at a point is defined to be the intersection of the variety with a small sphere centred at the point. The Euler characteristic of the link leads to local topological characterisation of real algebraic varieties in law dimensions. We prove in the paper that not only the Euler characteristic, but also the stronger virtual Poincaré polynomial is well-defined for the link at a point of an affine algebraic variety.