论文标题
通过LMO函数的同源气缸上的$ y $滤光的Abelian商
Abelian quotients of the $Y$-filtration on the homology cylinders via the LMO functor
论文作者
论文摘要
我们通过Mod $ \ Mathbb {Z} $减少LMO函数的Mod $ \ Mathbb {Z} $降低了同源气缸的$ y $滤光到扭转模块。我们对托雷利群体下部中央系列的同态限制并不能通过莫里塔对约翰逊同态的完善来考虑。我们用它表明，封闭表面的约翰逊内核的阿贝利亚化具有扭转元素。我们还确定了第三个分级的$ y_3 \ Mathcal {ic} _ {g，1}/y_4 $的$ y $ -filtration。
We construct a series of homomorphisms from the $Y$-filtration on the monoid of homology cylinders to torsion modules via the mod $\mathbb{Z}$ reduction of the LMO functor. The restriction of our homomorphism to the lower central series of the Torelli group does not factor through Morita's refinement of the Johnson homomorphism. We use it to show that the abelianization of the Johnson kernel of a closed surface has torsion elements. We also determine the third graded quotient $Y_3\mathcal{IC}_{g,1}/Y_4$ of the $Y$-filtration.
