Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771832 | Journal of Algebra | 2017 | 14 Pages |
Abstract
The main goal of this note is to provide evidence that the first rational homology of the Johnson subgroup Kg,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 H1(Kg,1,Q) with respect to the augmentation ideal in the rational group algebra of Z2g 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kevin Kordek,