Positive loops of loose Legendrian embeddings and applications
Guogang Liu
Abstract
In this paper, we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a partial order on Cont0(M, ξ), called strong orderability, and prove that overtwisted contact manifolds are not strongly orderable.
Topics & Concepts
Contractible spaceSubmanifoldMathematicsPure mathematicsOrder (exchange)CombinatoricsBusinessFinanceGeometric Analysis and Curvature FlowsMathematical Dynamics and FractalsGeometric and Algebraic Topology