The Johnson Cokernel and the Enomoto-Satoh invariant

Jim Conant

The Johnson Cokernel and the Enomoto-Satoh invariant

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1306.3698 v2 pith:3A7AVVCY submitted 2013-06-16 math.QA math.RT

Jim Conant This is my paper · ORCID

classification math.QAmath.RT

keywords enomoto-satohtracecokerneljohnsonpartrankauthorboundary

verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments

read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

One-dimensionality of certain cocycles for the detection of the Johnson cokernel
math.AT 2025-07 accept novelty 4.0 of 10

The vertex-graded 1-cocycles of the ribbon graph complex RGC1 are one-dimensional and spanned by the graph G1 corresponding to the Enomoto-Satoh trace.

Pith tools