We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES.
- Authors
HENRY, MICHAEL B.; RUTHERFORD, DAN
- Abstract
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 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.
- Subjects
COMBINATORICS; MATHEMATICAL sequences; MATHEMATICAL complexes; LINEAR systems; HOMOLOGY theory; GEOMETRIC analysis
- Publication
Communications in Contemporary Mathematics, 2013, Vol 15, Issue 2, p-1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199712500599