Generalized Johnson homomorphisms for extended N-series

JOURNAL OF ALGEBRA

卷:510

Article

Habiro, Kazuo¹  Massuyeau, Gwenael^2,3,4,5 

[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

[2] Univ Strasbourg, IRMA, F-67084 Strasbourg, France

[3] CNRS, F-67084 Strasbourg, France

[4] Univ Bourgogne Franche Comte, IMB, F-21000 Dijon, France

[5] CNRS, F-21000 Dijon, France

关键词: Groups;    Graded Lie algebras;    N-series;    Lower central series;    Automorphism groups of free groups;    Mapping class groups of surfaces;    Johnson homomorphisms;    Andreadakis-Johnson filtrations;   

DOI  :  10.1016/j.jalgebra.2018.05.031

来源: Elsevier

【 摘 要 】

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 an extended 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free