Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909045493858304 |
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| author | Blakey, Kenneth Porcelli, Noah |
| author_facet | Blakey, Kenneth Porcelli, Noah |
| contents | 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 criterion, in terms of the pair-of-pants product and the BV operator on symplectic cohomology, for when this MU lift cannot be obtained via base change from the sphere spectrum; moreover, we give examples where this holds. Finally, we use this non-base change criterion to detect examples of non-trivial higher-dimensional complex cobordism classes of relative Gromov-Witten type moduli spaces in the context of a smooth complex projective variety relative to an ample smooth divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06620 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch Blakey, Kenneth Porcelli, Noah Symplectic Geometry Algebraic Geometry Algebraic Topology 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 criterion, in terms of the pair-of-pants product and the BV operator on symplectic cohomology, for when this MU lift cannot be obtained via base change from the sphere spectrum; moreover, we give examples where this holds. Finally, we use this non-base change criterion to detect examples of non-trivial higher-dimensional complex cobordism classes of relative Gromov-Witten type moduli spaces in the context of a smooth complex projective variety relative to an ample smooth divisor. |
| title | Bulk-deformations, Floer complex bordism, and Grothendieck-Riemann-Roch |
| topic | Symplectic Geometry Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2605.06620 |