|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
A
landscape of contact manifolds via rational SFT
Agustin Moreno and Zhengyi Zhou |
|
Geometry & Topology 29 (2025) 3465–3565
|
 |
Abstract |
|
We define a hierarchy functor from the exact symplectic cobordism category to a totally ordered set from a (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 , 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 . 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. |
Keywords
symplectic field theory, symplectic cobordism, bi-Lie
infinity algebra
|
Mathematical Subject Classification
Primary: 53D10, 53D35, 53D42
|
References |
Publication
Received: 11 April 2022
Revised: 13 October 2024
Accepted: 30 November 2024
Published: 10 October 2025
Proposed: Yakov Eliashberg
Seconded: Leonid Polterovich, Mohammed Abouzaid
|
Authors |
| Agustin Moreno | |
| Institute for Advanced Study Princeton, NJ United States |
Heidelberg Universität Heidelberg Germany |
| Zhengyi Zhou | |
| Morningside Center of
Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China |
|
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
