{"paper":{"title":"Integration of Cocycles and Lefschetz Number Formulae for Differential Operators","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.QA","authors_text":"Ajay C. Ramadoss","submitted_at":"2009-04-13T00:26:18Z","abstract_excerpt":"Let ${\\mathcal E}$ be a holomorphic vector bundle on a complex manifold $X$ such that $\\dim_{{\\mathbb C}}X=n$. Given any continuous, basic Hochschild $2n$-cocycle $\\psi_{2n}$ of the algebra ${\\rm Diff}_n$ of formal holomorphic differential operators, one obtains a $2n$-form $f_{{\\mathcal E},\\psi_{2n}}(\\mathcal D)$ from any holomorphic differential operator ${\\mathcal D}$ on ${\\mathcal E}$. We apply our earlier results [J. Noncommut. Geom. 2 (2008), 405-448; J. Noncommut. Geom. 3 (2009), 27-45] to show that $\\int_X f_{{\\mathcal E},\\psi_{2n}}({\\mathcal D})$ gives the Lefschetz number of $\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1891","kind":"arxiv","version":3},"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"}