Pachner move and affine volume-preserving geometry in .
In this paper we emphasize Deligne's theory of weights, in order to prove that some stratifications of algebraic varieties are perfect. In particular, we study in some detail the Bialynicki-Birula's stratifications and the stratifications considered by F. Kirwan to compute the cohomology of symplectic or geometric quotients. Finally we also appoint the motivic formulation of this approach, which contains the Hodge theoretic formulation.
The goal of this article is to show some examples of topological manifolds: planes and spheres in Euclidean space. In doing it, the article introduces the stereographic projection [25].