Moment maps, symplectomorphism groups and compatible complex structures

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In this paper we apply Donaldson's general moment map framework for the action of a symplectomorphism group on the corresponding space of compatible (almost) complex structures to the case of rational ruled surfaces. This gives a new approach to understanding the topology of their symplectomorphism groups, based on a result of independent interest: the space of compatible integrable complex structures on any symplectic rational ruled surface is (weakly) contractible. We also explain how in general, under this condition, there is a direct relationship between the topology of a symplectomorphism group, the deformation theory of compatible complex structures and the groups of complex automorphisms of these complex structures.
To appear in the issue of the Journal of Symplectic Geometry devoted to the Stare Jablonki conference proceedings

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Symplectic Geometry, Algebraic Topology, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/75834

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0507382
 http://arxiv.org/abs/math/0507382

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arXiv