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We introduce the notion of a {\\em spin profile} as an obstruction class of extending the group action on Lagrangian submanifold to the one on its spin structure, which is a group cohomology class in $H^2(G;\\Z/2)$. For a class of Lagrangian submanifolds which have the same spin profiles, we define a finite group action on their Fukaya category. In consequence, we obta"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.4573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-07-17T10:49:16Z","cross_cats_sorted":[],"title_canon_sha256":"4fd80d8de6f8d017c29326361a0a994875d1f30f7133e021ba3df125ec861001","abstract_canon_sha256":"039c5b72b6c7cff4d9e33d2836e5591f22ead3e7d4d0ff9e7131c68cebd6182f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:41.714119Z","signature_b64":"Gog0WURqNywhdQCNg6IQ+hu/spifTXJkmWDvSEEYVWFdYAhzj0SWWgvWWFbS09R0DRahFNrSNKVri0QiPTUZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4ba8c492cc10d4b065a8d22565482176d5ce59e6478cbc681beea7239db5261","last_reissued_at":"2026-05-18T00:14:41.713505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:41.713505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite group actions on Lagrangian Floer theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Cheol-Hyun Cho, Hansol Hong","submitted_at":"2013-07-17T10:49:16Z","abstract_excerpt":"We construct finite group actions on Lagrangian Floer theory when symplectic manifolds have finite group actions and Lagrangian submanifolds have induced group actions. 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