A landscape of contact manifolds via rational SFT
We define a hierarchy functor from the exact symplectic cobordism category to a totally ordered set from a BL∞ (Bi-Lie) formalism of the rational symplectic field theory (RSFT). The hierarchy functor consists of three levels of structures, namely algebraic planar torsion, order of semidilation and p...
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| Auteurs principaux: | , |
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| Format: | Article (Journal) |
| Langue: | anglais |
| Publié: |
10 October 2025
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| In: |
Geometry & topology
Year: 2025, Volume: 29, Numéro: 7, Pages: 3465-3565, [1-2] |
| ISSN: | 1364-0380 |
| DOI: | 10.2140/gt.2025.29.3465 |
| Accès en ligne: | Verlag, kostenfrei, Volltext: https://doi.org/10.2140/gt.2025.29.3465 Verlag, kostenfrei, Volltext: https://msp.org/gt/2025/29-7/p02.xhtml 
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| Notes sur l'auteur: | Agustin Moreno, Zhengyi Zhou |
| Résumé: | We define a hierarchy functor from the exact symplectic cobordism category to a totally ordered set from a BL∞ (Bi-Lie) formalism of the rational symplectic field theory (RSFT). The hierarchy functor consists of three levels of structures, namely algebraic planar torsion, order of semidilation and planarity, all taking values in N∪{∞}, where algebraic planar torsion can be understood as the analogue of the algebraic torsion of Latschev and Wendl (2011) in the context of RSFT. The hierarchy functor is well-defined through a partial construction of RSFT and is within the scope of established virtual techniques. We develop computational tools for those functors and prove that all three of them are surjective. In particular, the planarity functor is surjective in all dimension ≥3. Then we use the hierarchy functor to study the existence of exact cobordisms. We discuss examples including iterated planar open books, spinal open books, affine varieties with uniruled compactification and links of singularities. |
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| Description: | Veröffentlicht: 10. Oktober 2025 Gesehen am 25.02.2026 |
| Description matérielle: | Online Resource |
| ISSN: | 1364-0380 |
| DOI: | 10.2140/gt.2025.29.3465 |