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15 June 2009 Compatible complex structures on symplectic rational ruled surfaces
Miguel Abreu, Gustavo Granja, Nitu Kitchloo
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Duke Math. J. 148(3): 539-600 (15 June 2009). DOI: 10.1215/00127094-2009-033

Abstract

In this article, we study the topology of the space Iω of complex structures compatible with a fixed symplectic form ω, using the framework of Donaldson. By comparing our analysis of the space Iω with results of McDuff on the space Jω of compatible almost complex structures on rational ruled surfaces, we find that Iω is contractible in this case.

We then apply this result to study the topology of the symplectomorphism group of a rational ruled surface, extending results of Abreu and McDuff

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Miguel Abreu. Gustavo Granja. Nitu Kitchloo. "Compatible complex structures on symplectic rational ruled surfaces." Duke Math. J. 148 (3) 539 - 600, 15 June 2009. https://doi.org/10.1215/00127094-2009-033

Information

Published: 15 June 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1171.53053
MathSciNet: MR2527325
Digital Object Identifier: 10.1215/00127094-2009-033

Subjects:
Primary: 53D35
Secondary: 32G05 , 57R17 , 57S05

Rights: Copyright © 2009 Duke University Press

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Vol.148 • No. 3 • 15 June 2009
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