Structures of the cohomology rings of the Torelli group and Lagrangian mapping class groups

Johnson-Morita理论在研究被称为拉格朗日映射类群的曲面映射类群的子群中起着重要的作用。我们确定了有理的第五个和第六个Johnson同态的像，并研究了相关李代数的结构(与Shigeyuki Morita和Masaaki Suzuki共同工作)。特别地，我们确定了所谓的“结合情形”的简单化，并证明了黎曼曲面的模空间的最高有理同调群为零。

Johnson-Morita theory plays an important role in the study of subgroups of mapping class groups of surfaces called Lagrangian mapping class groups. We determined the images of the rational fifth and sixth Johnson homomorphisms and studied the structures of related Lie algebras(Joint work with Shigeyuki Morita and Masaaki Suzuki). In particular, we determined the abelianization of so-called "the associative case" and showed that the highest rational homology group of the moduli space of Riemann surfaces vanish.