A Lagrangian spine in the Milnor fiber of a plane curve singularity

Time: 15:00 - 16:00 (VN time), 11st May

Online: (google meet) https://meet.google.com/yyb-zhod-hdy?authuser=3&hl=vi

Abstract: Joint work with Pablo Portilla Cuadrado. Given an equation f(x,y) = 0 for a singularity of a plane curve, we define the total spine as the union of trajectories of the gradient of -|f|^2 converging to the origin. The spine of a Milnor fiber is its intersection with the total spine, which is always a strong deformation retract.
We explicitly describe the topology of the spine in terms of an embedded resolution, and the polar curve. Under generic conditions, the spine of a Milnor fiber is a graph. In addition, we define a spine in the Milnor fiber at radius zero, which is always a graph. In further later work we intend to generalize these results in more dimensions, and apply this work in studying monodromy.