Giovanni Gaiffi
(Scuola Normale Superiore, Pisa)
Real models of arrangements and conical stratifications
Abstract: [ps] [pdf]: Let us consider a central subspace and half-space arrangement ${\mathcal A}$ in an euclidean vector space $V$ and let ${\mathcal M}({\mathcal A})$ be its complement. We construct some compactifications for the $C^{\infty}$ manifold ${\mathcal M}({\mathcal A})/{\mathbb R} ^+$. They turn out to be $C^{\infty}$ manifolds with corners equipped with a nice combinatorial description of the boundary. This generalizes a construction described by Kontsevich in ``Deformation quantization of Poisson manifolds, I.'' (q-alg/9709040). Then we extend the construction to more general objects, i.e. stratified real manifolds whose stratification locally ``looks like'' the one induced by a subspace and half-space arrangement.