Finiteness properties of the Johnson subgroups

JOURNAL OF ALGEBRA

卷:477

Article

Kordek, Kevin¹ 

[1] Texas A&M Univ, Dept Math, Mailstop 3368, College Stn, TX 77843 USA

关键词: Mapping class groups;    The Johnson filtration;    Group cohomology;    Alexander invariants;   

DOI  :  10.1016/j.jalgebra.2016.09.024

来源: Elsevier

【 摘 要 】

The main goal of this note is to provide evidence that the first rational homology of the Johnson subgroup K-9,(1) of the mapping class group of a genus g surface with one marked point is finite-dimensional. Building on work of Dimca Papadima [4], we use symplectic representation theory to show that, for all g > 3, the completion of H-1 (K-9,(1), Q) with respect to the augmentation ideal in the rational group algebra of Z(29) is finite-dimensional. We also show that the terms of the Johnson filtration of the mapping class group have infinite dimensional rational homology in some degrees in almost all genera, generalizing a result of Akita.(C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free