An example concerning Hamiltonian groups of self product, I

Abstract

We show that $(S^2\times S^2, ω_0 \oplus λω_0)$, with $λ> 1$, is an example of symplectic manifold $(X, ω)$ such that the $π_1 Ham(X \times X, ω\oplus -ω)$ contains extra elements than those from $π_1 Ham(X, ω) \times π_1 Ham(X, -ω)$.

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