Let $(S^2,\omega )$ be a symplectic sphere, and let $\tau :S^2\to S^2$ be an anti‐symplectic involution of $(S^2,\omega )$. We consider the product $(S^2,\omega )\times (S^2,\omega )$ endowed with the anti‐symplectic involution $\tau \times \tau$, and study the space of monotone anti‐invariant symplectic forms on this four‐manifold. We show that this space is disconnected. In addition, during the course of the proof, we produce a diffeomorphism of $\mathsf{Gr}(2,4)$ which induces the identity map on all homology and homotopy groups, but which is not homotopic to the identity.

中文翻译：

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S2×S2上的无限多非同位素实辛形式

让 $（{\mathrm{小号}}^2，\omega ）$ 成为一个辛球，让 $\tau ：{\mathrm{小号}}^2\to {\mathrm{小号}}^2$ 成为 $（{\mathrm{小号}}^2，\omega ）$。我们考虑产品$（{\mathrm{小号}}^2，\omega ）\times （{\mathrm{小号}}^2，\omega ）$ 具备反象征对合 $\tau \times \tau$，并研究这四个流形上单调抗不变辛形式的空间。我们表明该空间是断开的。此外，在证明过程中，我们产生了$\mathsf{GR}（2，4）$ 其在所有同源性和同型性基团上诱导出同一性图，但是与该同一性不是同位的。