{"paper":{"title":"Anderson duality of topological modular forms and its differential-geometric manifestations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.KT"],"primary_cat":"math.AT","authors_text":"Mayuko Yamashita, Yuji Tachikawa","submitted_at":"2023-05-10T14:27:48Z","abstract_excerpt":"We construct and study a morphism of spectra implementing the Anderson duality of topological modular forms ($\\mathrm{TMF}$). Its differential version will then be introduced, allowing us to pair elements of $\\pi_d\\mathrm{TMF}$ with spin manifolds whose boundaries are equipped with string structure. A few negative-degree elements of $\\pi_d\\mathrm{TMF}$ will then be constructed using the theory of $\\mathrm{RO}(G)$-graded $\\mathrm{TMF}$, and will be identified using the differential pairing. We also discuss a conjecture relating vertex operator algebras and negative-degree elements of $\\pi_d\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.06196","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.06196/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"}