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Mathematics > Symplectic Geometry

arXiv:1803.05717 (math)
[Submitted on 15 Mar 2018 (v1), last revised 24 Jun 2019 (this version, v3)]

Title:A Chekanov-Eliashberg algebra for Legendrian graphs

Authors:Byung Hee An, Youngjin Bae
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Abstract:We define a differential graded algebra for Legendrian graphs and tangles in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas from Legendrian contact homology. The construction is distinguished from other versions of Legendrian contact algebra by the vertices of Legendrian graphs. A set of countably many generators and a generalized notion of equivalence are introduced for invariance. We show a van Kampen type theorem for the differential graded algebras under the tangle replacement. Our construction recovers many known algebraic constructions of Legendrian links via suitable operations at the vertices.
Comments: 94 pages
Subjects: Symplectic Geometry (math.SG); Geometric Topology (math.GT)
MSC classes: Primary 53D42, 57R17, Secondary 57M15
Cite as: arXiv:1803.05717 [math.SG]
  (or arXiv:1803.05717v3 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.1803.05717
Related DOI: https://doi.org/10.1112/topo.12138

Submission history

From: Byung Hee An [view email]
[v1] Thu, 15 Mar 2018 13:04:51 UTC (164 KB)
[v2] Sun, 16 Sep 2018 16:17:37 UTC (217 KB)
[v3] Mon, 24 Jun 2019 11:27:50 UTC (240 KB)
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