{"paper":{"title":"Obstruction theory and the level $n$ elliptic genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrew Senger","submitted_at":"2022-03-25T16:20:23Z","abstract_excerpt":"Given a height $\\leq 2$ Landweber exact $\\mathbb{E}_\\infty$-ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the Ando criterion admits a unique lift to an $\\mathbb{E}_\\infty$-complex orientation $\\mathrm{MU} \\to E$. As a consequence, we give a short proof that the level $n$ elliptic genus lifts uniquely to an $\\mathbb{E}_\\infty$-complex orientation $\\mathrm{MU} \\to \\mathrm{tmf}_1 (n)$ for all $n \\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13743","kind":"arxiv","version":1},"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/2203.13743/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"}