Asian Journal of Mathematics
Volume 16 (2012)
Lagrangian unknottedness in Stein surfaces
Pages: 1 – 36
We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.
Stein manifolds; Lagrangian submanifolds; Hamiltonian diffeomorphisms; symplectic Dehn twists
2010 Mathematics Subject Classification