2023/08/12 by Sen, Balarka
#32S60 (Secondary) #57R17 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2308.06551
This article provides an exposition of Emmy Murphy's work on loose Legendrian embeddings. After a brief review of the rudiments of contact topology, we state and discuss some foundational results from the theory of h-principles, providing many relevant examples from contact topology on the way. We then proceed to prove Murphy's h-principle for loose Legendrian embeddings. We also provide an accessible exposition of some background material from microlocal sheaf theory. As applications, we demonstrate the existence of non-loose Legendrian embeddings, and prove a version of Gromov's nonsqueezing theorem for loose charts.