Inductively collapsing Fukaya categories and flexibility

GAUGE-TOPOLOGY-SYMPLECTIC

Speaker:

Emmy Murphy - Northwestern

Abstract:

A Weinstein manifold is a symplectic manifold which admits a Lagrangian skeleton, and associated to any Weinstein manifold is its wrapped Fukaya category, a powerful algebraic invariant. One important case is that the wrapped category of C^n is trivial. The talk will discuss a partial converse: if X is any Weinstein 6-manifold which is contractible, admitting an arboreal skeleton so that the wrapped category is inductively collapsing, then X is symplectomorphic to C^3. A large portion of the talk will be defining the notion of inductively collapsing: this is a purely algebraic condition, but it depends on a presentation of the wrapped category, which itself comes from a chosen Lagrangian skeleton.