The Johnson Cokernel and the Enomoto-Satoh invariant
Quantum Algebra
2016-01-20 v2 Representation Theory
Abstract
We study the cokernel of the Johnson homomorphism for the mapping class group of a surface with one boundary component. A graphical trace map simultaneously generalizing trace maps of Enomoto-Satoh and Conant-Kassabov-Vogtmann is given, and using technology from the author's work with Kassabov and Vogtmann, this is is shown to detect a large family of representations which vastly generalizes series due to Morita and Enomoto-Satoh. The Enomoto-Satoh trace is the rank 1 part of the new trace. The rank 2 part is also investigated.
Keywords
Cite
@article{arxiv.1306.3698,
title = {The Johnson Cokernel and the Enomoto-Satoh invariant},
author = {Jim Conant},
journal= {arXiv preprint arXiv:1306.3698},
year = {2016}
}
Comments
Added a reference to forthcoming work with Kassabov