Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 6 (2015), 3323-3353.
Equivalence classes of augmentations and Morse complex sequences of Legendrian knots
Let be a Legendrian knot in with the standard contact structure. In earlier work of Henry, a map was constructed from equivalence classes of Morse complex sequences for , which are combinatorial objects motivated by generating families, to homotopy classes of augmentations of the Legendrian contact homology algebra of . Moreover, this map was shown to be a surjection. We show that this correspondence is, in fact, a bijection. As a corollary, homotopic augmentations determine the same graded normal ruling of and have isomorphic linearized contact homology groups. A second corollary states that the count of equivalence classes of Morse complex sequences of a Legendrian knot is a Legendrian isotopy invariant.
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3323-3353.
Received: 25 July 2014
Revised: 10 April 2015
Accepted: 15 April 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Henry, Michael B; Rutherford, Dan. Equivalence classes of augmentations and Morse complex sequences of Legendrian knots. Algebr. Geom. Topol. 15 (2015), no. 6, 3323--3353. doi:10.2140/agt.2015.15.3323. https://projecteuclid.org/euclid.agt/1510841069