Title: Homotopy decomposition of a group of symplectomorphisms of S^2\times S^2
Authors: Silvia Anjos and Gustavo Granja
AMS Classification numbers: 57S05, 57R17, 55R35
Address of Authors:
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais
1049-001 Lisboa
Portugal
Email address of Authors:
sanjos@math.ist.utl.pt
ggranja@math.ist.utl.pt
Abstract: We continue the analysis started by Abreu, McDuff and Anjos of the
topology of the group of symplectomorphisms of $S^2 \times S^2$ when the ratio
of the areas of the two spheres lies in the interval (1,2]. We express the
group, up to homotopy, as the amalgam of certain of its compact Lie subgroups.
We use this to compute the homotopy type of the classifying space of the
group of symplectomorphisms and the corresponding ring of characteristic classes
for symplectic fibrations.