Tori in four-dimensional Milnor fibres

Princeton/IAS Symplectic Geometry Seminar
Topic:Tori in four-dimensional Milnor fibres
Speaker:Ailsa Keating
Affiliation:Massachusetts Institute of Technology
Date:Friday, November 8
Time/Room:1:30pm - 2:30pm/Fine 322, Princeton University

The Milnor fibre of any isolated hypersurface singularity contains exact Lagrangian spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for simple singularities, it is known that the only possible exact Lagrangians are spheres. I will explain how to construct exact Lagrangian tori in the Milnor fibres of all non-simple singularities of real dimension four. Time allowing, I will use these to give examples of fibres whose Fukaya categories are not generated by vanishing cycles.