{"paper":{"title":"Integration over complex manifolds via Hochschild homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"Ajay C. Ramadoss","submitted_at":"2007-07-31T04:11:58Z","abstract_excerpt":"Given a holomorphic vector bundle $\\cale$ on a connected compact complex manifold X, [FLS] construct a $\\compl$-linear functional $I_{\\cale}$ on $\\hh{2n}{\\compl}$. This is done by constructing a linear functional on the 0-th completed Hochschild homology $\\choch{0}{(\\dif(\\cale))}$ of the sheaf of holomorphic differential operators on $\\cale$ using topological quantum mechanics. They show that this functional is $\\int_X$ if $\\cale$ has non zero Euler characteristic. They conjecture that this functional is $\\int_X$ for all $\\cale$.\n  A subsequent work [Ram] by the author proved that the linear f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4528","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":""},"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"}