Compatible complex structures on symplectic rational ruled surfaces

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In this paper we study the topology of the space $\I_ω$ of complex structures compatible with a fixed symplectic form $ω$, using the framework of Donaldson. By comparing our analysis of the space $\I_ω$ with results of McDuff on the space $\cat J_ω$ of compatible almost complex structures on rational ruled surfaces, we find that $\I_ω$ 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.
Sign mistake in the formula for the cohomology in twisted case fixed. Reorganized sections 4 and 5 and added more detail to proofs. To appear in Duke Math. Journal

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Symplectic Geometry, Algebraic Topology, Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/218960

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610436
 http://arxiv.org/abs/math/0610436

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arXiv