Stability of the symplectomorphism groups of rational surfaces
Published in Mathematische Annalen, 2023
Recommended citation: Anjos, S., Li, J., Li, TJ. et al. Stability of the symplectomorphism groups of rational surfaces. Math. Ann. 389, 85–119 (2024). https://doi-org.proxy1.lib.uwo.ca/10.1007/s00208-023-02643-5 https://doi.org/10.1007/s00208-023-02643-5
We apply Zhang’s almost Kähler Nakai–Moishezon theorem and Li–Zhang’s comparison of $J$-symplectic cones to establish a stability result for the symplectomorphism group of a rational 4-manifold $M$ with Euler number up to 12. As a corollary, we also derive a stability result for the space of embedded symplectic balls in $M$. A noteworthy feature of our approach is that we systematically explore various spaces and groups associated to a symplectic cohomology class u rather than with a single symplectic form $\omega$. To this end, we prove a weaker version of the tamed $J$-inflation procedures of D. McDuff and O. Buse that fixes a gap in their original formulations.