Geometry & Topology
- Geom. Topol.
- Volume 12, Number 4 (2008), 1921-1993.
The rational homotopy type of a blow-up in the stable case
Suppose 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 which is the blow-up of along . Assume that and that is injective. We construct an algebraic model of the rational homotopy type of the blow-up from an algebraic model of the embedding and the Chern classes of the normal bundle. This implies that if the space is simply connected then the rational homotopy type of depends only on the rational homotopy class of and on the Chern classes of the normal bundle.
Geom. Topol., Volume 12, Number 4 (2008), 1921-1993.
Received: 25 January 2006
Accepted: 26 March 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55P62: Rational homotopy theory
Secondary: 14F35: Homotopy theory; fundamental groups [See also 14H30] 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D05: Symplectic manifolds, general
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