{"paper":{"title":"Addendum to \"The Johnson cokernel and the Enomoto-Satoh invariant\": The ES-trace detects all top-level partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"James Conant","submitted_at":"2016-10-13T04:50:35Z","abstract_excerpt":"The degree $d$ part of the cokernel $\\mathsf C_d$ of the Johnson homomorphism decomposes into irreducible $\\mathrm{SP}$-modules indexed by partitions of $d-2r$ for $r\\geq 0$: $$\\mathsf C_d\\cong \\mathsf C_d(d)\\oplus \\mathsf C_d(d-2)\\oplus\\cdots.$$ In this addendum we calculate $\\mathsf{C}_d(d)$ precisely: it is isomorphic to the $\\mathrm{GL}(V)$-decomposition of a space of coinvariants $(V^{\\otimes d})_{D_{2d}}$, and the isomorphism is induced by Enomoto and Satoh's trace map. This establishes Conjecture 7.2 of the paper \"The Johnson Cokernel and the Enomoto-Satoh invariant.\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05220","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}