A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES

作者：Henry Michael B^*; Rutherford Dan

来源：Communications in Contemporary Mathematics, 2013, 15(2): 1250059.

DOI：10.1142/S0219199712500599

• Legendrian knots
• generating families
• contact homology
• augmentations
• Morse complex sequences

For a Legendrian knot L subset of R-3, 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 equivalent MCS's we prove the corresponding linearized complexes of the DGA are isomorphic. If the MCS has a standard form, then we show that our DGA agrees with the Chekanov-Eliashberg DGA after changing coordinates by an augmentation.

• 出版日期2013-4