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arXiv · 1611.07436

Symplectic $(-2)$ spheres and the symplectomorphism group of small rational 4-manifolds, I

Jun Li·Tian-Jun Li
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Abstract

Let $(X,ω)$ be a symplectic rational 4 manifold. We study the space of tamed almost complex structures $\mathcal{J}_ω$ using a fine decomposition via smooth rational curves and a relative version of the infinite-dimensional Alexander duality. This decomposition provides new understandings of both the variation and stability of the symplectomorphism group $Symp(X,ω)$ when deforming $ω$. In particular, we compute the rank of $π_1(Symp(X,ω))$ with Euler number $χ(X)\leq 7$ in terms of the number $N$ of -2 symplectic sphere classes.

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Jun Li, Tian-Jun Li. 2019-11-26. Symplectic $(-2)$ spheres and the symplectomorphism group of small rational 4-manifolds, I. https://arxiv.org/abs/1611.07436

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