{"paper":{"title":"Cohomological $\\chi$-independence for Higgs bundles and Gopakumar-Vafa invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Naoki Koseki, Tasuki Kinjo","submitted_at":"2021-12-19T03:37:37Z","abstract_excerpt":"The aim of this paper is two-fold: Firstly, we prove Toda's $\\chi$-independence conjecture for Gopakumar--Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we introduce the BPS cohomology for moduli spaces of Higgs bundles of rank $r$ and Euler characteristic $\\chi$ which are not necessary coprime, and show that it does not depend on $\\chi$. This result extends the Hausel--Thaddeus conjecture on the $\\chi$-independence of E-polynomials proved by Mellit, Groechenig--Wyss--Ziegler and Yu in two ways: we obtain an isomorphism of mixed Hodge modules on the Hitchin base"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10053","kind":"arxiv","version":2},"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/2112.10053/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"}