Isaac Hasse-Armengol

On the rank of $π_1(\mathrm{Symp}_0)$

We show that for any positive integer $k$ there exists a closed symplectic $4$-manifold $(M,ω)$, such that $H^1_\mathrm{dR}(M;\mathbb{R})$ is a $k$-dimensional real vector space and its Flux group is equal to $H^1_\mathrm{dR}(M_1;\mathbb{Z})$.