Symplectic mapping class groups of blowups of tori

Abstract

Let $\omega$ be a Kähler form on the real 4-torus $T^4$. Suppose that $\omega$ satisfies an irrationality condition that can be achieved by an arbitrarily small perturbation of $\omega$. This note shows that the smoothly trivial symplectic mapping class group of the one-point symplectic blowup of $(T^4,\omega )$ is infinitely generated.