{"paper":{"title":"Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For Liouville manifolds the complexified lift of symplectic cohomology to complex cobordism equals the version bulk-deformed by the Chern character.","cross_cats":["math.AG","math.AT"],"primary_cat":"math.SG","authors_text":"Kenneth Blakey, Noah Porcelli","submitted_at":"2026-05-07T17:34:40Z","abstract_excerpt":"Given a Liouville manifold, we compute a Floer-homotopical invariant -- the complexification of the lift of symplectic cohomology to complex cobordism -- in terms of a classical Floer-theoretic invariant, namely, symplectic cohomology bulk-deformed by the Chern character. We do this by giving an explicit model for the complexified homotopy groups of the MU-module spectrum associated to a complex-oriented flow category and proving a ``homotopy coherent'' version of the classical Grothedieck-Riemann-Roch theorem. Using the aforementioned relation, we establish a computable cohomological criterio"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Given a Liouville manifold, we compute a Floer-homotopical invariant -- the complexification of the lift of symplectic cohomology to complex cobordism -- in terms of a classical Floer-theoretic invariant, namely, symplectic cohomology bulk-deformed by the Chern character.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That an explicit model exists for the complexified homotopy groups of the MU-module spectrum associated to a complex-oriented flow category, and that a homotopy-coherent version of the Grothendieck-Riemann-Roch theorem holds for this model (as invoked in the abstract to establish the main computation).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes relation between MU-lifted symplectic cohomology and bulk-deformed version via homotopy coherent GRR, yielding computable criterion for non-trivial complex cobordism classes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For Liouville manifolds the complexified lift of symplectic cohomology to complex cobordism equals the version bulk-deformed by the Chern character.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0369375434c85f5fabc18d1ed7c57a6dd537472529ddc694bb016e793c28f112"},"source":{"id":"2605.06620","kind":"arxiv","version":2},"verdict":{"id":"eada9859-9205-467e-b5fb-55611c8f1b5e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T16:45:53.369255Z","strongest_claim":"Given a Liouville manifold, we compute a Floer-homotopical invariant -- the complexification of the lift of symplectic cohomology to complex cobordism -- in terms of a classical Floer-theoretic invariant, namely, symplectic cohomology bulk-deformed by the Chern character.","one_line_summary":"Establishes relation between MU-lifted symplectic cohomology and bulk-deformed version via homotopy coherent GRR, yielding computable criterion for non-trivial complex cobordism classes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That an explicit model exists for the complexified homotopy groups of the MU-module spectrum associated to a complex-oriented flow category, and that a homotopy-coherent version of the Grothendieck-Riemann-Roch theorem holds for this model (as invoked in the abstract to establish the main computation).","pith_extraction_headline":"For Liouville manifolds the complexified lift of symplectic cohomology to complex cobordism equals the version bulk-deformed by the Chern character."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06620/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:19.278496Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:33:02.829091Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1b0609639d81f5ecdec7bbd35cb5ac66657b24e93466be4e5f01f01173fbc8d6"},"references":{"count":16,"sample":[{"doi":"","year":null,"title":"Foundation of Floer homotopy theory I: flow categories","work_id":"8b072937-2067-4d11-85dd-7a02c0f4c5b5","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Symplectic cohomology and viterbo’s theorem.arXiv preprint arXiv:1312.3354","work_id":"fb3109f5-e745-4599-8800-5a1d848750eb","ref_index":2,"cited_arxiv_id":"1312.3354","is_internal_anchor":true},{"doi":"","year":null,"title":"On arborealization, Maslov data, and lack thereof","work_id":"04f66238-41d9-449d-82e4-091973e6c167","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"[BB25] Kenneth Blakey and Ciprian M. 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