Product structures for Legendrian contact homology
نویسندگان
چکیده
منابع مشابه
Legendrian Contact Homology in P × R
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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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 that a null–homologous transverse knot K in the complement of an overtwisted disk in a contact 3–manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self–linking number of K with respect to S satisfies sl(K,S) = −χ(S). In particular, every null–homologous topological knot type in an overtwisted contact manifold can be represented...
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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: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2010
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004110000460