Equivalence relations for homology cylinders and the core of the Casson invariant
Equivalence relations for homology cylinders and the core of the Casson invariant
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同调圆柱的等价关系和卡森不变量的核心
DOI：
10.1090/s0002-9947-2013-05818-7
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发表时间：
2011
影响因子：
1.3
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
G. Massuyeau;Jean
设R为具有一个边界分量的g属紧致定向曲面。R上的同调柱面通过映射柱面构造嵌入到R的托雷利群I中，形成了一个单调IC。如果M‘是由M中的任意曲面S与属于S的Torelli群的下中心级数的同同态在M中“扭曲”得到的，则M’和M'是y_k等价的。IC上的j_k等价关系用Johnson滤波的第k项以类似的方式定义。本文用三个经典不变量刻画y_3等价：(1)对R基群的第三个幂零商的作用，(2)相对Alexander多项式的二次部分，(3)Casson不变量的副产物。同样，我们证明了j_3等价由(1)和(2)分类。我们还证明了Casson不变量（最初是由Morita在I的Johnson滤除的第二项上定义的）的核具有唯一的扩展（到IC的相应子拟元），该扩展由y_3等价和映射类群作用保存。
Let R be a compact oriented surface of genus g with one boundary component. Homology cylinders over R form a monoid IC into which the Torelli group I of R embeds by the mapping cylinder construction. Two homology cylinders M and M' are said to be Y_k-equivalent if M' is obtained from M by "twisting" an arbitrary surface S in M with a homeomorphim belonging to the k-th term of the lower central series of the Torelli group of S. The J_k-equivalence relation on IC is defined in a similar way using the k-th term of the Johnson filtration. In this paper, we characterize the Y_3-equivalence with three classical invariants: (1) the action on the third nilpotent quotient of the fundamental group of R, (2) the quadratic part of the relative Alexander polynomial, and (3) a by-product of the Casson invariant. Similarly, we show that the J_3-equivalence is classified by (1) and (2). We also prove that the core of the Casson invariant (originally defined by Morita on the second term of the Johnson filtration of I) has a unique extension (to the corresponding submonoid of IC) that is preserved by Y_3-equivalence and the mapping class group action.
沿 3 流形中的 Brunnian 连接进行手术
DOI：
--
发表时间：
2006
期刊：
プレプリント RIMS-1538
影响因子：
--
作者：
Meilhan;Jean-Baptiste
通讯作者：
Jean-Baptiste
拉格朗日配边函数 LMO 不变量
DOI：
--
发表时间：
2008
期刊：
Geom. Topol 12
影响因子：
--
作者：
D. Cheptea;K. Habiro and G. Massuyeau
通讯作者：
K. Habiro and G. Massuyeau