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arXiv · 1911.00961

Stability of the symplectomorphism group of rational surfaces

Silvia Anjos·Jun Li·Tian-Jun Li·Martin Pinsonnault
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Abstract

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 $ω$. 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.

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Silvia Anjos, Jun Li, Tian-Jun Li, Martin Pinsonnault. 2023-06-03. Stability of the symplectomorphism group of rational surfaces. https://arxiv.org/abs/1911.00961

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