Uniqueness of Lagrangians in $T^*RP2$

Abstract

We present a new and elementary proof of the fact that any Lagrangian RP 2 in T * RP 2 is Hamiltonian isotopic to the identity. The proof mirrors the analogous result for T * S 2 found in [12], using surgery to turn Lagrangian spheres to symplectic ones. The heart of the arguement is proving the folklore fact that the unit cotangent disc bundle of RP 2 compactifies to CP 2 .