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The
rational homotopy type of a blow-up in the stable case
Pascal Lambrechts and Donald Stanley |
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Geometry & Topology 12 (2008) 1921–1993
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Abstract |
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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. |
Keywords
blow-up, shriek map, rational homotopy, symplectic manifold
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Mathematical Subject Classification 2000
Primary: 55P62
Secondary: 14F35, 53C15, 53D05
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References |
Publication
Received: 25 January 2006
Accepted: 26 March 2008
Published: 5 July 2008
Proposed: Bill Dwyer
Seconded: Haynes Miller, Tom Goodwillie
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Authors |
| Pascal Lambrechts | |
| Chercheur qualifié au FNRS Université Catholique de Louvain Institut Mathématique Chemin du Cyclotron, 2 B-1348 Louvain-la-Neuve BELGIUM |
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| Donald Stanley | |
| University of Regina Department of Mathematics College West 307.14 Regina, Saskatchewan Canada S4S 0A2 |
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