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We show that if a Legendrian knot in a standard contact space ℝ 3  possesses a generating family, then there exists an augmentation of the Chekanov–Eliashberg differential graded algebra so that the associated linearized contact homology (LCH) is isomorphic to singular homology groups arising from the generating family. In this setting, we show that 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 implies normal ruling.

Generating families and Legendrian contact homology in the standard contact space