The rational homotopy type of a blow-up in the stable case

Details The rational homotopy type of a blow-up in the stable case The rational homotopy type of a blow-up in the stable case

2007-06-10

arxiv.org/abs/0706.1363v1

Mathematics

Algebraic Topology

Scientific paper

Suppose that f:V->W is an embedding of closed oriented manifolds whose normal bundle has the structure of a complex vector bundle. It is well known in both complex and symplectic geometry that one can then construct a manifold W' which is the blow-up of W along V. Assume that dim(W)>2.dim(V)+2 and that H^1(f) is injective. We construct an algebraic model of the rational homotopy type of the blow-up W' from an algebraic model of the embedding and the Chern classes of the normal bundle. This implies that if the space W is simply connected then the rational homotopy type of W' depends only on the rational homotopy class of f and on the Chern classes of the normal bundle.

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