An example concerning Hamiltonian groups of self product, I

Abstract

We show that $(S^2\times S^2,{\omega }_0\oplus \lambda {\omega }_0)$, with $\lambda >1$, is an example of symplectic manifold $(X,\omega )$ such that the ${\pi }_{1}Ham(X\times X,\omega \oplus -\omega )$ contains extra elements than those from ${\pi }_{1}Ham(X,\omega )\times {\pi }_{1}Ham(X,-\omega )$.

This is the first of two short articles. They originally form one paper. After submission, it was split into two parts by the request of the Journal. They appeared in African Diaspora Journal of Mathematics