Joint IAS/PU Symplectic Geometry Seminar

An exact Lagrangian in a cotangent bundle that coincides with
a cotangent fiber outside a compact set, and is disjoint from at least
one cotangent fiber is called a nearby Lagrangian fiber. I will explain
joint work in preparation with Yash Deshmukh and Alex Pieloch, showing
that any nearby Lagrangian fiber in $T^{*}\mathbb{CP}^{2}$ or $T^{*}(S^{n-k} \times \mathbb{R}^{k})$ is
smoothly isotopic to a cotangent fiber rel boundary in the complement of
the missed fiber. These results follows from a more general homotopy
rigidity result for exact Lagrangian fillings of unknots in subcritical
Weinstein manifolds.