论文标题
$ s^2 \ times s^2 $上的许多非同位素真实形式
Infinitely many non-isotopic real symplectic forms on $S^2 \times S^2$
论文作者
论文摘要
令$（s^2，ω）$为符号球体，让$τ\ colon s^2 \ to s^2 $为$（s^2，ω）$的反隔离率。我们考虑赋予抗惊性的$（s^2，ω）\ times（s^2，ω）$ $（S^2，ω）$，并赋予了反透明度的$τ\ timesτ$，并研究了这四个manifold的单调抗不变符号形式的空间。我们证明了这个空间是断开连接的。此外，在证明过程中，我们产生了格拉斯曼尼亚（2,4）的差异性，该差异诱导了所有同源性和同型组的身份图，但对身份不同义。
Let $(S^2,ω)$ be a symplectic sphere, and let $τ\colon S^2 \to S^2$ be an anti-symplectic involution of $(S^2,ω)$. We consider the product $(S^2,ω) \times (S^2,ω)$ endowed with the anti-symplectic involution $τ\times τ$, 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 the grassmannian (2,4) which induces the identity map on all homology and homotopy groups, but which is not homotopic to the identity.
