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Equivalence classes of
augmentations and Morse complex sequences of Legendrian
knots
Michael B Henry and Dan Rutherford |
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Algebraic & Geometric Topology 15 (2015) 3323–3353
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Abstract |
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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. |
Keywords
invariants, Legendrian knots, augmentations, Morse complex
sequences, generating families, differential graded
algebra, Legendrian isotopy, contact structure, normal
ruling
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Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 57M25, 53D40
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References |
Publication
Received: 25 July 2014
Revised: 10 April 2015
Accepted: 15 April 2015
Published: 12 January 2016
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Authors |
| Michael B Henry | |
| Department of Mathematics Siena College 515 Loudon Road Loudonville, NY 12211 USA |
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| Dan Rutherford | |
| Department of Mathematics Ball State University 2000 W University Ave Muncie, IN 47306 USA |
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