{"paper":{"title":"Relative Calabi-Yau structure on microlocalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.SG","authors_text":"Christopher Kuo, Wenyuan Li","submitted_at":"2024-08-07T20:56:16Z","abstract_excerpt":"For an oriented manifold $M$ and a compact subanalytic Legendrian $\\Lambda \\subseteq S^*M$, we construct a canonical strong smooth relative Calabi--Yau structure on the microlocalization at infinity and its left adjoint $m_\\Lambda^l: \\operatorname{\\mu sh}_\\Lambda(\\Lambda) \\rightleftharpoons \\operatorname{Sh}_\\Lambda(M)_0 : m_\\Lambda$ between compactly supported sheaves on $M$ with singular support on $\\Lambda$ and microsheaves on $\\Lambda$. We also construct a canonical strong Calabi-Yau structure on microsheaves $\\operatorname{\\mu sh}_\\Lambda(\\Lambda)$. Our approach does not require local pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.04085","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/2408.04085/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"}