Abstract:

 

Spherical twist is one of the major sources of autoequivalences of the derived Fukaya category.

It is induced geometrically by a symplectomorphism, called spherical Dehn twist, compactly supported near a Lagrangian sphere submanifold. Huybrechts and Thomas predicted an upgraded version of this correspondence between projective twist on the categories and projective Dehn twist on the symplectic manifolds.

We will explain a proof of this conjecture via the technique of Lagrangian cobordism/correspondence.

This is a joint work with Weiwei Wu.