A Chekanov-Eliashberg algebra for Legendrian graphs
arXiv:1803.05717 · doi:10.1112/topo.12138
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.
arXiv comment94 pages
References in corpus (11)
- Covariantly functorial wrapped Floer theory on Liouville sectors
- Duality between Lagrangian and Legendrian invariants
- On partially wrapped Fukaya categories
- A complete knot invariant from contact homology
- Arboreal Singularities
- Liouville hypersurfaces and connect sum cobordisms
- Rational Symplectic Field Theory for Legendrian knots
- A bordered Chekanov-Eliashberg algebra
- Arboreal singularities from Lefschetz fibrations
- Legendrian theta-graphs
- Legendrian singular links and singular connected sums