Translator Disclaimer
2008 The rational homotopy type of a blow-up in the stable case
Pascal Lambrechts, Donald Stanley
Geom. Topol. 12(4): 1921-1993 (2008). DOI: 10.2140/gt.2008.12.1921

Abstract

Suppose f:VW 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 dimW2dimV+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.

Citation

Download Citation

Pascal Lambrechts. Donald Stanley. "The rational homotopy type of a blow-up in the stable case." Geom. Topol. 12 (4) 1921 - 1993, 2008. https://doi.org/10.2140/gt.2008.12.1921

Information

Received: 25 January 2006; Accepted: 26 March 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1153.55010
MathSciNet: MR2431012
Digital Object Identifier: 10.2140/gt.2008.12.1921

Subjects:
Primary: 55P62
Secondary: 14F35, 53C15, 53D05

Rights: Copyright © 2008 Mathematical Sciences Publishers

JOURNAL ARTICLE
73 PAGES


SHARE
Vol.12 • No. 4 • 2008
MSP
Back to Top