Generating families and Legendrian contact homology in the standard contact space

Abstract

We show that if a Legendrian knot in standard contact ${\bb R}^3$ possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology (LCH) is isomorphic to singular homology groups arising from the generating family. In this setting we show Sabloff's duality result for LCH may be viewed as Alexander duality. In addition, we provide an explicit construction of a generating family for a front diagram with graded normal ruling and give a new approach to augmentation $\Rightarrow$ normal ruling.

Revised version, to appear in Journal of Topology. Following referee suggestions, parts of sections 4 and 6 have been removed for more efficient exposition

References in corpus (2)

• Generating family invariants for Legendrian links of unknots
• Augmentations and Rulings of Legendrian Knots

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