Generating families and Legendrian contact homology in the standard contact space
نویسندگان
چکیده
منابع مشابه
Generating Families and Legendrian Contact Homology in the Standard Contact Space
We show that if a Legendrian knot in standard contact R3 possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology is isomorphic to singular homology groups arising from the generating family. We discuss the relationship between normal rulings, augmentations, and generating families. In particular, we provid...
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We consider S1–families of Legendrian knots in the standard contact R3 . We define the monodromy of such a loop, which is an automorphism of the Chekanov–Eliashberg contact homology of the starting (and ending) point. We prove this monodromy is a homotopy invariant of the loop (Theorem 1.1). We also establish techniques to address the issue of Reidemeister moves of Lagrangian projections of Leg...
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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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We define the contact homology for Legendrian submanifolds in standard contact (2n + 1)-space using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. This homology provides new invariants of Legendrian isotopy which indicate that the theory of Legendrian isotopy is very rich. Indeed, in [4] the homology is used to detect infinite families of pairwise non...
متن کاملLEGENDRIAN SUBMANIFOLDS IN R2n+1 AND CONTACT HOMOLOGY
Contact homology for Legendrian submanifolds in standard contact (2n + 1)space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. The homology provides new invariants of Legendrian isotopy. These invariants show that the theory of Legendrian isotopy is very rich. For example, they detect infinite families of pairwise non-isotop...
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ژورنال
عنوان ژورنال: Journal of Topology
سال: 2011
ISSN: 1753-8416
DOI: 10.1112/jtopol/jtq033