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- W1982805502 abstract "We construct a version of rational Symplectic Field Theory for pairs $(X,L)$, where $X$ is an exact symplectic manifold, where $Lsubset X$ 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 $Lambdasubset Y$ is a Legendrian submanifold of a contact manifold then the spectral sequences associated to $(YtimesR,Lambda_k^stimesR)$, where $YtimesR$ is the symplectization of $Y$ and where $Lambda_k^ssubset Y$ is the Legendrian submanifold consisting of $s$ parallel copies of $Lambda$ subdivided into $k$ subsets, give Legendrian isotopy invariants of $Lambda$." @default.
- W1982805502 created "2016-06-24" @default.
- W1982805502 creator A5080159470 @default.
- W1982805502 date "2008-01-01" @default.
- W1982805502 modified "2023-10-18" @default.
- W1982805502 title "Rational symplectic field theory over ℤ2 for exact Lagrangian cobordisms" @default.
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- W1982805502 doi "https://doi.org/10.4171/jems/126" @default.
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