Generalized Johnson homomorphisms for extended N-series
Generalized Johnson homomorphisms for extended N-series
复制标题
扩展 N 级数的广义 Johnson 同态
DOI：
10.1016/j.jalgebra.2018.05.031
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发表时间：
2018
影响因子：
0.9
通讯作者：
Gwenael Massuyeau
中科院分区：
文献类型：
--
作者：
Kazuo Habiro;Gwenael Massuyeau
紧的定向曲面的映射类群的Johnson滤子是由曲面的基本群的幂零商上的作用的核组成的降级数。Johnson滤子的每一项都有一个Johnson同态，其核是滤子中的下一项。在这篇文章中，我们考虑了一种一般情况，其中一个群作用于一个群，它具有一个称为扩展N-系列的滤子。在这一一般情况下，我们发展了一种Johnson同态理论，包括许多已知的原始Johnson同态的变体以及几个新的变体。
The Johnson filtration of the mapping class group of a compact, oriented surface is the descending series consisting of the kernels of the actions on the nilpotent quotients of the fundamental group of the surface. Each term of the Johnson filtration admits a Johnson homomorphism, whose kernel is the next term in the filtration. In this paper, we consider a general situation where a group acts on a group with a filtration called anextended N-series. We develop a theory of Johnson homomorphisms in this general setting, including many known variants of the original Johnson homomorphisms as well as several new variants.