Odd-dimensional Charney-Davis conjecture

More than once we have heard that the Charney-Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres.Comment: 3 pages, no figure

A two-cocycle on the group of symplectic diffeomorphisms

We investigate a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifolds defined by Ismagilov, Losik, and Michor and investigate its properties. We provide both vanishing and non-vanishing results and applications to foliated symplectic bundles and to Hamiltonian actions of finitely generated groups.Comment: 16 pages, no figure