Planar Legendrian graphs
Copyright policy )Planar Legendrian graphs
We prove two results on the classification of trivial Legendrian embeddings $g: G \rightarrow (S^3,��_{std})$ of planar graphs. First, the oriented Legendrian ribbon $R_g$ and rotation invariant $\text{rot}_g$ are a complete set of invariants. Second, if $G$ is 3-connected or contains $K_4$ as a minor, then the unique trivial embedding of $G$ is Legendrian simple.
23 pages, 9 figures
- University of Georgia Press United States
- Marymount University United States
Legendrian simple, Mathematics - Geometric Topology, Legendrian graphs, contact topology, FOS: Mathematics, Contact manifolds (general theory), convex surface theory, Geometric Topology (math.GT), Relations of low-dimensional topology with graph theory, 53D10, 57M15, 05C10, Planar graphs; geometric and topological aspects of graph theory
Legendrian simple, Mathematics - Geometric Topology, Legendrian graphs, contact topology, FOS: Mathematics, Contact manifolds (general theory), convex surface theory, Geometric Topology (math.GT), Relations of low-dimensional topology with graph theory, 53D10, 57M15, 05C10, Planar graphs; geometric and topological aspects of graph theory
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