Augmentations and ruling polynomials for Legendrian graphs

Byung Hee An; Youngjin Bae; Tao Su

doi:10.2140/agt.2022.22.2079

Abstract

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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Byung Hee An. Youngjin Bae. Tao Su. "Augmentations and ruling polynomials for Legendrian graphs." Algebr. Geom. Topol. 22 (5) 2079 - 2185, 2022. https://doi.org/10.2140/agt.2022.22.2079

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Received: 31 December 2019; Revised: 15 October 2020; Accepted: 28 March 2021; Published: 2022

First available in Project Euclid: 10 November 2022

zbMATH: 1511.57029

MathSciNet: MR4503334

Digital Object Identifier: 10.2140/agt.2022.22.2079

Subjects:

Primary: 57R17

Secondary: 05C31 , 57M15

Keywords: augmentation variety , Chekanov–Eliashberg DGA , Legendrian graphs , ruling polynomial

Abstract

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