Betti numbers of semi-Pfaffian sets Original Research Article

We consider semi-Pfaffian sets defined as closed sign conditions on a compact Pfaffian variety image of dimension k′ in image If we consider a Pfaffian chain (f1,…,fℓ) of length ℓ and degree α on its domain image we prove that all compact semi-Pfaffian sets defined on image by a sign condition on a family {p1,…,ps} of Pfaffian functions that are polynomials of degree β in the Pfaffian chain (f1,…,fℓ), have the sum of their Betti numbers bounded by sk′ 2ℓ(ℓ−1)/2 O(kβ+min(ℓ,k)α)k+ℓ.