Compatible complex structures on symplectic rational ruled surfaces

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dc.creatorAbreu, Miguel
dc.creatorGranja, Gustavo
dc.creatorKitchloo, Nitu
dc.date2006-10-13
dc.date2009-02-09
dc.date.accessioned2026-07-07T12:39:00Z
dc.date.available2026-07-07T12:39:00Z
dc.descriptionIn 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.
dc.descriptionSign 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
dc.identifierhttps://arxiv.org/abs/math/0610436
dc.identifierhttp://arxiv.org/abs/math/0610436
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218960
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.titleCompatible complex structures on symplectic rational ruled surfaces
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