Augmentations and ruling polynomials for Legendrian graphs

Byung Hee An; Youngjin Bae; Tao Su

doi:10.2140/agt.2022.22.2079

Augmentations and ruling polynomials for Legendrian graphs

Byung Hee An, Youngjin Bae, Tao Su

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2079-2185
Number of pages	107
Journal	Algebraic and Geometric Topology
Volume	22
Issue number	5
DOIs	https://doi.org/10.2140/agt.2022.22.2079
State	Published - 2022

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10.2140/agt.2022.22.2079

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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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AB - 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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JO - Algebraic and Geometric Topology

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Augmentations and ruling polynomials for Legendrian graphs

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