Evaluation fibrations and topology of symplectomorphisms

There are two main results. The first states that isotropy subgroups of groups acting transitively on a rationally hyperbolic spaces have infinitely generated rational cohomology algebra. Using this fact, we prove that the analogous statement holds for groups of symplectomorphisms of certain blow-ups.Comment: 10 pages, no figure

Symplectic configurations

We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral symplectic manifolds. We construct the classifyng space \B of symplectic integral configurations. The properties of the classifying map \B --> BSymp(M,w) are examined. The universal symplectic bundle over \B has a natural connection whose holonomy group is isomorphic to the enlarged Hamiltonian group recently defined by McDuff. The space \B is identified with the classifying space of an extension of certain subgroup of the symplectomorphism group.Comment: 25 pages, no figure

The autonomous norm on Ham(R2n) is bounded

We thank the Center for Advanced Studies in Mathematics at Ben Gurion University for supporting the visit of the second author at BGU. We also thank the anonymous referee for useful comments.Peer reviewedPostprin