Moment maps, symplectomorphism groups and compatible complex structures
Abstract
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.
Cite
@article{arxiv.math/0507382,
title = {Moment maps, symplectomorphism groups and compatible complex structures},
author = {Miguel Abreu and Gustavo Granja and Nitu Kitchloo},
journal= {arXiv preprint arXiv:math/0507382},
year = {2007}
}
Comments
To appear in the issue of the Journal of Symplectic Geometry devoted to the Stare Jablonki conference proceedings