## Geometry & Topology

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

#### Abstract

Suppose $f:V→W$ 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 $dimW≥2dimV+3$ and that $H1(f)$ 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.

#### Article information

Source
Geom. Topol., Volume 12, Number 4 (2008), 1921-1993.

Dates
Accepted: 26 March 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800118

Digital Object Identifier
doi:10.2140/gt.2008.12.1921

Mathematical Reviews number (MathSciNet)
MR2431012

Zentralblatt MATH identifier
1153.55010

#### Citation

Lambrechts, Pascal; Stanley, Donald. The rational homotopy type of a blow-up in the stable case. Geom. Topol. 12 (2008), no. 4, 1921--1993. doi:10.2140/gt.2008.12.1921. https://projecteuclid.org/euclid.gt/1513800118

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