Symplectomorphism groups and almost complex structures

Details Symplectomorphism groups and almost complex structures Symplectomorphism groups and almost complex structures

2000-10-27

arxiv.org/abs/math/0010274v2

Enseignment Math 38 (2001) 1--30

Mathematics

Symplectic Geometry

24 pages, with minor corrections

Scientific paper

This paper studies groups of symplectomorphisms of ruled surfaces for symplectic forms with varying cohomology class. This class is characterized by the ratio R of the size of the base to that of the fiber. By considering appropriate spaces of almost complex structures, we investigate how the topological type of these groups changes as R increases. If the base is a sphere, this changes precisely when R passes an integer, and for general bases it stabilizes as R goes to infinity. Our results extend and make more precise some of the conclusions of Abreu--McDuff concerning the rational homotopy type of these groups for rational ruled surfaces.

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