A Chekanov-Eliashberg algebra for Legendrian graphs

• Main Authors: An, Byung Hee, Bae, Youngjin
• Format: Journal Article
• Language: English
• Published: 24-06-2019
• Subjects: Mathematics - Geometric Topology; Mathematics - Symplectic Geometry
• DOI: 10.48550/arxiv.1803.05717

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.