The Johnson cokernel and the Enomoto–Satoh invariant

Conant, James

doi:10.2140/agt.2015.15.801

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The Johnson cokernel and the Enomoto–Satoh invariant

James Conant

Algebraic & Geometric Topology 15 (2015) 801–821

DOI: 10.2140/agt.2015.15.801

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 and Satoh and Conant, Kassabov and 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 and Satoh. The Enomoto–Satoh trace is the rank- $1$ part of the new trace, and it is here that the new series of representations is found. The rank- $2$ part is also investigated, though a fuller investigation of the higher-rank case is deferred to another paper.

Keywords

Johnson homomorphism, Enomoto–Satoh invariant, Johnson cokernel

Mathematical Subject Classification 2010

Primary: 17B40

Secondary: 20C15, 20F28

References

Publication

Received: 23 December 2013

Revised: 5 July 2014

Accepted: 7 July 2014

Published: 22 April 2015

Authors

James Conant
Department of Mathematics University of Tennessee 227 Ayres Hall 1403 Circle Drive Knoxville, TN 37996 USA
http://www.math.utk.edu/~jconant/

Volume 15, issue 2 (2015)