2012/09/13 by Adam Knapp, Knapp, Adam
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.1209.3045
arxiv created 2012/09/13 · arxiv updated 2012/09/17
We show that, for any two orientable smooth open 4-manifolds X0,X1 which are homeomorphic, their cotangent bundles T^*X0,T^*X1 are symplectomorphic with their canonical symplectic structure. In particular, for any smooth manifold R homeomorphic to ℝ4, the standard Stein structure on T^*R is Stein homotopic to the standard Stein structure on T^*ℝ4 = ℝ8. We use this to show that any exotic ℝ4 embeds in the standard symplectic ℝ8 as a Lagrangian submanifold. As a corollary, we show that ℝ8 has uncountably many smoothly distinct foliations by Lagrangian ℝ4s with their standard smooth structure.