Rational SFT, Linearized Legendrian Contact Homology, and Lagrangian Floer Cohomology
2012 (English)In: Perspectives in Analysis, Geometry, and Topology: On the Occasion of the 60th Birthdayof Oleg Viro / [ed] Ilia Itenberg, Burglind Jöricke, Mikael Passare, Springer Science+Business Media B.V., 2012, 109-145 p.Conference paper (Refereed)
We relate the version of rational symplectic field theory for exact Lagrangian cobordisms introduced in  to linearized Legendrian contact homology. More precisely, if L ⊂ Xis an exact Lagrangian submanifold of an exact symplectic manifold with convex end Λ ⊂ Y, where Yis a contact manifold and Λis a Legendrian submanifold, and if Lhas 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 Seidel , this equality in combination with a version of Lagrangian Floer cohomology of Lleads us to a conjectural exact sequence that in particular implies that if X=Cn , then the linearized Legendrian contact cohomology of Λ ⊂ S 2n − 1is 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  in terms of the resulting isomorphism.
Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2012. 109-145 p.
, Progress in Mathematics, ISSN 0743-1643 ; 296
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-167294DOI: 10.1007/978-0-8176-8277-4_6ISI: 000307264800007ISBN: 978-0-8176-8276-7OAI: oai:DiVA.org:uu-167294DiVA: diva2:483180
Perspectives in Analysis, Geometry, and Topology, Stockholm, Sweden, May 19-25 2008