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

On the Cohomology of Classifying Spaces of Groups of Homeomorphisms

Acknowledgements. The present work was built upon the papers [3,8]. The author thanks his previous co-authors Dusa McDuff, Swiatoslaw Gal and Alex Tralle for discussions. The author thanks Dusa McDuff and Oldrich Spacil for useful comments on a preliminary version of this paper. Any remaining mistakes are the author’s responsibility. The author also thanks the anonymous referee for useful comments.Peer reviewedPostprin

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

On the algebraic independence of Hamiltonian characteristic classes

We prove that Hamiltonian characteristic classes defined as fibre integrals of powers of the coupling class are algebraically independent for generic coadjoint orbits.Comment: 9 pages, no figure