关于Metoki类的一个猜想的肯定回答
An affirmative answer to a conjecture for Metoki class
摘要：
在“The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversatile symplectic foliations”arXiv：0910.3414中，Kotschick和Morita证明了$\ds\HGF{7}{2}{}{8}$中的Gel'fand-Kalinin-Fuks类被分解为某个叶上同调类$η$和一个transversatile辛类$ω$的乘积$η\wedge ω$。我们表明，同样的公式适用于Metoki类，这是一个非平凡的元素在$\ds \HGF{9}{2}{}{14}$。这个结果由Kotschick和Morita证明，他们研究了Kontsevich的辛叶理的特征类。我们的证明依赖于Groebner基理论使用计算机计算。
英文摘要：
In "The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversely symplectic foliations" arXiv:0910.3414, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds\HGF{7}{2}{}{8}$ is decomposed as a product $η\wedge ω$ of some leaf cohomology class $η$ and a transverse symplectic class $ω$. We show that the same formula holds for Metoki class, which is a non-trivial element in $\ds \HGF{9}{2}{}{14}$. The result was conjectured by Kotschick and Morita, where they studied characteristic classes of symplectic foliations due to Kontsevich. Our proof depends on Groebner Basis theory using computer calculations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
