Generating Families and Legendrian Contact Homology in the Standard Contact Space
نویسندگان
چکیده
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 provide an explicit construction of a generating family for a front diagram with graded normal ruling and give a method for computing linearized contact homology groups using the combinatorics of a normal ruling.
منابع مشابه
LEGENDRIAN 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...
متن کاملTHE CONTACT HOMOLOGY OF LEGENDRIAN SUBMANIFOLDS IN R2n+1
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 کاملNON-ISOTOPIC LEGENDRIAN SUBMANIFOLDS IN R2n+1
The contact homology, rigorously defined in [7], is computed for a number of Legendrian submanifolds in standard contact (2n+1)-space. The homology is used to detect infinite families of pairwise non-isotopic Legendrian n-spheres, n-tori, and surfaces which are indistinguishable using previously known invariants.
متن کاملNon-isotopic Legendrian Submanifolds in R
In the standard contact (2n+1)-space when n > 1, we construct infinite families of pairwise non-Legendrian isotopic, Legendrian n-spheres, n-tori and surfaces which are indistinguishable using classically known invariants. When n is even these are the first known examples of non-Legendrian isotopic, Legendrian submanifolds of (2n + 1)-space. Such constructions indicate a rich theory of Legendri...
متن کاملContact homology and one parameter families of Legendrian knots
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...
متن کامل