Algebraic & Geometric Topology

The Johnson cokernel and the Enomoto–Satoh invariant

James Conant

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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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 2 (2015), 801-821.

Dates
Received: 23 December 2013
Revised: 5 July 2014
Accepted: 7 July 2014
First available in Project Euclid: 28 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895790

Digital Object Identifier
doi:10.2140/agt.2015.15.801

Mathematical Reviews number (MathSciNet)
MR3342677

Zentralblatt MATH identifier
1361.20028

Subjects
Primary: 17B40: Automorphisms, derivations, other operators
Secondary: 20C15: Ordinary representations and characters 20F28: Automorphism groups of groups [See also 20E36]

Keywords
Johnson homomorphism Enomoto–Satoh invariant Johnson cokernel

Citation

Conant, James. The Johnson cokernel and the Enomoto–Satoh invariant. Algebr. Geom. Topol. 15 (2015), no. 2, 801--821. doi:10.2140/agt.2015.15.801. https://projecteuclid.org/euclid.agt/1511895790


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