Open Access
December 2005 Moment maps, symplectomorphism groups and compatible complex structures
Miguel Abreu Abreu, Gustavo Granja, Nitu Kitchloo
J. Symplectic Geom. 3(4): 655-670 (December 2005).


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.


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Miguel Abreu Abreu. Gustavo Granja. Nitu Kitchloo. "Moment maps, symplectomorphism groups and compatible complex structures." J. Symplectic Geom. 3 (4) 655 - 670, December 2005.


Published: December 2005
First available in Project Euclid: 1 August 2006

zbMATH: 1162.53062
MathSciNet: MR2235857

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 4 • December 2005
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