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A PERSONAL TOUR THROUGH SYMPLECTIC TOPOLOGY AND MIGUEL ABREU
 

Summary: A PERSONAL TOUR THROUGH SYMPLECTIC TOPOLOGY AND
GEOMETRY
MIGUEL ABREU
1. Introduction
In this survey I will present a very personal tour through symplectic topology and geometry,
describing the following three paths and the way most of my work fits in them.
(i) Gromov's Compactness Theorem for pseudo-holomorphic curves in symplectic manifolds
([23]) and the topology of symplectomorphism groups of rational ruled surfaces (sections
2 and 3, references [1, 2]).
(ii) Atiyah-Guillemin-Sternberg's Convexity Theorem for the moment map of Hamiltonian
torus actions ([9, 25]) and K¨ahler geometry of toric orbifolds in symplectic coordinates
(sections 4 and 5, references [3, 4, 5]).
(iii) Donaldson's moment map framework for the action of the symplectomorphism group on
the space of compatible almost complex structures ([17]) and the topology of the space
of compatible integrable complex structures of a rational ruled surface (sections 6 and 7,
references [6, 7]).
Acknowledgments. I would like to thank my advisor, Yakov Eliashberg, and the collaborators
I had in the work described in this survey: Dusa McDuff, Gustavo Granja and Nitu Kitchloo. My
mathematical life has been much easier because of them.
2. Pseudo-holomorphic Curves in Symplectic Manifolds

  

Source: Abreu, Miguel - Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa

 

Collections: Mathematics