Homotopy decomposition of a group of symplectomorphisms of S² × S²

2003/03/07 by Sı́lvia Anjos, Silvia Anjos, Anjos, Silvia +2
Mathematics · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.SG #msc:55R35 #msc:57R17 #msc:57S05

paper · pdf · doi:10.48550/arxiv.math/0303091

18 pages

arxiv created 2003/03/07 · arxiv updated 2009/11/30

Abstract

We continue the analysis, started by Abreu, McDuff and Anjos, of the topology of the group of symplectomorphisms of S² × S² 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.

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