Algebra Seminar 

18/10/2002, 15:00 — 16:00 — Room P4.35, Mathematics Building
Pascal Lambrechts, Université Catholique de Louvain

On the rational homotopy type of blow-up of submanifolds

There is a general construction of ''blowing-up'' a manifold $W$ along a submanifold $V$. This construction has applications both in algebraic geometry and in symplectic topology. In this talk we show that the rational homotopy type of such a blow-up is completely determined by the rational homotopy class of the embdedding and the Chern classes of its normal bundle, at least when $\dim (W)\ge 2\dim (V)+4$. In fact a computable model of the rational homotopy type of the blow-up $\tilde{W}$ can be explicitely described. This construction gives many examples of non-formal simply-connect symplectic manifolds.