Augmentations and rulings of Legendrian knots

A connection between holomorphic and generating family invariants of Legendrian knots is established; namely, that the existence of a ruling (or decomposition) of a Legendrian knot is equivalent to the existence of an augmentation of its contact homology. This result was obtained independently and using different methods by Fuchs and Ishkhanov [12]. Close examination of the proof yields an algorithm for constructing a ruling given an augmentation. Finally, a condition for the existence of an augmentation in terms of the rotation number is obtained.