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Topology of Symplectomorphism Groups of Miguel Abreu

Summary: Topology of Symplectomorphism Groups of
× S2
Miguel Abreu
Stanford University
final version
December 4, 1996
0 Introduction
In dimension 4, due to non-existence of adequate tools, very little is known
about the topology of groups of diffeomorphisms. For example, it is unknown
if the group of compactly supported diffeomorphisms of R4
is connected.
The situation is much better if one wants to study groups of symplectomor-
phisms. This is due to the existence of powerful tools, going by the name of
"pseudo-holomorphic curve techniques" and introduced in symplectic geometry
by M.Gromov in his seminal paper of 1985 [5]. Gromov proved in that paper,
among several other remarkable results, the contractibility of the group of com-
pactly supported symplectomorphisms of R4
with its standard symplectic form


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


Collections: Mathematics