Rational Symplectic Field Theory over Z_2 for exact Lagrangian cobordisms
| dc.creator | Ekholm, Tobias | |
| dc.date | 2006-12-01 | |
| dc.date.accessioned | 2026-07-07T07:33:34Z | |
| dc.date.available | 2026-07-07T07:33:34Z | |
| dc.description | We construct a version of rational Symplectic Field Theory for pairs $(X,L)$, where $X$ is an exact symplectic manifold, where $L\subset X$ is an exact Lagrangian submanifold with components subdivided into $k$ subsets, and where both $X$ and $L$ have cylindrical ends. The theory associates to $(X,L)$ a $\Z$-graded chain complex of vector spaces over $\Z_2$, filtered with $k$ filtration levels. The corresponding $k$-level spectral sequence is invariant under deformations of $(X,L)$ and has the following property: if $(X,L)$ is obtained by joining a negative end of a pair $(X',L')$ to a positive end of a pair $(X'',L'')$, then there are natural morphisms from the spectral sequences of $(X',L')$ and of $(X'',L'')$ to the spectral sequence of $(X,L)$. As an application, we show that if $Λ\subset Y$ is a Legendrian submanifold of a contact manifold then the spectral sequences associated to $(Y\times\R,Λ_k^s\times\R)$, where $Y\times\R$ is the symplectization of $Y$ and where $Λ_k^s\subset Y$ is the Legendrian submanifold consisting of $s$ parallel copies of $Λ$ subdivided into $k$ subsets, give Legendrian isotopy invariants of $Λ$. | |
| dc.identifier | https://arxiv.org/abs/math/0612029 | |
| dc.identifier | http://arxiv.org/abs/math/0612029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119503 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 57R17; 53D12; 57R58; 53D40 | |
| dc.title | Rational Symplectic Field Theory over Z_2 for exact Lagrangian cobordisms | |
| dc.type | text |