{"paper":{"title":"Atiyah and Todd classes arising from integrable distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Maosong Xiang, Ping Xu, Zhuo Chen","submitted_at":"2017-11-30T06:43:57Z","abstract_excerpt":"In this paper, we study the Atiyah class and Todd class of the DG manifold $(F[1],d_F)$ corresponding to an integrable distribution $F \\subset T_{\\mathbb{K}} M = TM \\otimes_{\\mathbb{R}} \\mathbb{K}$, where $\\mathbb{K} = \\mathbb{R}$ or $\\mathbb{C}$. We show that these two classes are canonically identical to those of the Lie pair $(T_{\\mathbb{K}} M, F)$. As a consequence, the Atiyah class of a complex manifold $X$ is isomorphic to the Atiyah class of the corresponding DG manifold $(T^{0,1}_X[1],\\bar{\\partial})$. Moreover, if $X$ is a compact K\\\"ahler manifold, then the Todd class of $X$ is also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11253","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"}