{"paper":{"title":"Finite generation, algebraicity, and representation stability for homology of Torelli groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.RT"],"primary_cat":"math.GT","authors_text":"Alexander A. Gaifullin","submitted_at":"2026-06-11T16:07:29Z","abstract_excerpt":"We solve a long-standing problem of whether the homology groups of the Torelli subgroups $\\mathcal{I}_g\\le\\mathrm{Mod}_g$ are finitely generated in stable range. Namely, we prove that the group $H_k(\\mathcal{I}_g;\\mathbb{Z})$ is finitely generated, provided that $k\\le g-2$. Two main ingredients of our approach are as follows. First, we show that the action of any symplectic transvection $t_x\\in\\mathrm{Sp}_{2g}(\\mathbb{Z})$ on the homology of $\\mathcal{I}_g$ satisfies the following unipotency condition: $(t_x-1)^{k+1}H_k( \\mathcal{I}_g;\\mathbb{Z})=0$. The proof of this fact relies on the study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13517","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13517/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}