Homotopy Rigidity of Nearby Lagrangian Cocores

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∗ℂℙ2

or T∗(Sn−k×ℝk)

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.