Symplectomorphism groups and almost complex structures

By D. Mcduff. 2000

60 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e1b49836c0e4980a8e53594b026db2498d45816b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Martin Pinsonnault
2. Francois M. Lalonde
3. Jonathan D. Evans
4. T. Ekholm
5. P. Seidel

In Mathematical Physics

1. Martin Pinsonnault
2. Francois M. Lalonde
3. Jonathan D. Evans
4. T. Ekholm
5. P. Seidel

Citations in the corpus

• The topology of the space of symplectic balls in rational 4-manifolds (2002, methodology): “1In [ 14 ], McDuff applies this in the simpler context of the spaces Mµ and Mµ′.”