A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES

@article{Henry2013ACD,
  title={A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES},
  author={Michael B. Henry and Dan Rutherford},
  journal={Communications in Contemporary Mathematics},
  year={2013},
  volume={15},
  pages={1250059}
}
For a Legendrian knot L ⊂ ℝ3, with a chosen Morse complex sequence (MCS), we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MCS arises from a generating family F, we give a geometric interpretation of our chord paths as certain broken gradient trajectories which we call "gradient staircases". Given two… 
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