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Augmentations and ruling polynomials for Legendrian graphs

Byung Hee An, Youngjin Bae and Tao Su

Algebraic & Geometric Topology 22 (2022) 2079–2185

We study and show the equivalence between two Legendrian isotopy invariants associated to a (bordered) Legendrian graph: the augmentation number via point counting over a finite field for the augmentation variety of the associated Chekanov–Eliashberg differential graded algebra, and the ruling polynomial via combinatorics of the decompositions of the associated front projection.

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Legendrian graphs, Chekanov–Eliashberg DGA, augmentation variety, ruling polynomial
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 05C31, 57M15
Received: 31 December 2019
Revised: 15 October 2020
Accepted: 28 March 2021
Published: 25 October 2022
Byung Hee An
Department of Mathematics Education
Teachers College
Kyungpook National University
South Korea
Center for Geometry and Physics
Institute for Basic Science
Sout Korea
Youngjin Bae
Department of Mathematics
Incheon National University
South Korea
Tao Su
Department of Mathematics
École Normale Supérieure