Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology
| dc.creator | Ekholm, Tobias | |
| dc.date | 2009-02-25 | |
| dc.date.accessioned | 2026-07-07T12:46:42Z | |
| dc.date.available | 2026-07-07T12:46:42Z | |
| dc.description | We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\subset X$ is an exact Lagrangian submanifold of an exact symplectic manifold with convex end $Λ\subset Y$, where $Y$ is a contact manifold and $Λ$ is a Legendrian submanifold, and if $L$ has empty concave end, then the linearized Legendrian contact cohomology of $Λ$, linearized with respect to the augmentation induced by $L$, equals the rational SFT of $(X,L)$. Following ideas of P. Seidel, this equality in combination with a version of Lagrangian Floer cohomology of $L$ leads us to a conjectural exact sequence which in particular implies that if $X=\C^{n}$ then the linearized Legendrian contact cohomology of $Λ\subset S^{2n-1}$ is isomorphic to the singular homology of $L$. We outline a proof of the conjecture and show how to interpret the duality exact sequence for linearized contact homology of [6] in terms of the resulting isomorphism. | |
| dc.description | 32 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0902.4317 | |
| dc.identifier | http://arxiv.org/abs/0902.4317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221470 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D40; 53D35; 57R17 | |
| dc.title | Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology | |
| dc.type | text |