A duality exact sequence for legendrian contact homology
نویسندگان
چکیده
منابع مشابه
A Duality Exact Sequence for Legendrian Contact Homology
We establish a long exact sequence for Legendrian submanifolds L ⊂ P × R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L to P off of itself. In this sequence, the singular homology H∗ maps to linearized contact cohomology CH, which maps to linearized contact homology CH∗, which maps to singular homology. In particular, the sequence ...
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We show how to orient moduli spaces of holomorphic disks with boundary on an exact Lagrangian immersion of a spin manifold into complex n-space in a coherent manner. This allows us to lift the coefficients of the contact homology of Legendrian spin submanifolds of standard contact (2n + 1)-space from Z2 to Z. We demonstrate how the Z-lift provides a more refined invariant of Legendrian isotopy....
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A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P × R, where P is an exact symplectic manifold, is established. The class of such contact manifolds includes 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of Rn and, more generally, invariants of self t...
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Given a symplectic manifold (W,ω) with contact type boundary (M, ξ), one can define the symplectic homology of (W,ω) and the linearized contact homology of (M, ξ) with respect to its filling. We establish a Gysintype exact sequence relating these invariants and describe one of the maps therein in terms of rational holomorphic curves in the symplectization of (M, ξ).
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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 ⊂ X is an exact Lagrangian submanifold of an exact symplectic manifold with convex end Λ ⊂ Y , where Y is a contact manifold and Λ is a Legendrian submanifold, and if L has empty concave end, then the linearized Legendrian ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2009
ISSN: 0012-7094
DOI: 10.1215/00127094-2009-046