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arXiv · 1306.3698

The Johnson Cokernel and the Enomoto-Satoh invariant

Jim 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-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.

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Jim Conant. 2013-06-16. The Johnson Cokernel and the Enomoto-Satoh invariant. https://doi.org/10.2140/agt.2015.15.801

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