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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0904.1891","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2009-04-13T00:26:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0f1afaab4c66e194dd97f40814749c3e7dff32b3667d731f72caf4c04a6e6f36","abstract_canon_sha256":"1ced40450c607c4d8560b555f99a5b80afb06c3b04b5f4c34b0aadafd58ce43b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:29.995862Z","signature_b64":"QYm4JhJdO0C52y/FrjbpbSoxYW6eO6XuWmninJN60Klgg6uWUXltzsqQ8yXpeFlozHQ/hZuYSVFwMpTFsi3gAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b6c4f3d06b55321d9d9f43ab4777b34959f7073b9635acee9ab324397eb786e","last_reissued_at":"2026-05-18T04:31:29.995428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:29.995428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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