论文标题
$ l^{2} $ - 硬Lefschetz完整的符号歧管
$L^{2}$-hard Lefschetz complete symplectic manifolds
论文作者
论文摘要
对于完整的符号歧管$ m^{2n} $，我们在$ m^{2n} $上定义了$ l^{2} $ - 硬lefschetz属性。我们还证明，完整的符号歧管$ m^{2n} $满足$ l^{2} $ - 且仅当每个类别的$ l^{2} $ - 谐波形式包含$ l^{2} $ symplectic谐波形式时，仅当$ l^{2} $时。作为一个应用程序，如果$ m^{2n} $是一个封闭的符号抛物线歧管，它满足了硬Lefschetz属性，那么其Euler特性就满足了不等式$（-1）^{n}χ（m^{2n}）\ geq0 $。
For a complete symplectic manifold $M^{2n}$, we define the $L^{2}$-hard Lefschetz property on $M^{2n}$. We also prove that the complete symplectic manifold $M^{2n}$ satisfies $L^{2}$-hard Lefschetz property if and only if every class of $L^{2}$-harmonic forms contains a $L^{2}$ symplectic harmonic form. As an application, we get if $M^{2n}$ is a closed symplectic parabolic manifold which satisfies the hard Lefschetz property, then its Euler characteristic satisfies the inequality $(-1)^{n}χ(M^{2n})\geq0$.
