Cheol Hyun Cho, Floer Theory for the Variation Operator of an Isolated Singularity

The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define a new Floer cohomology, called monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the Seifert form. We discuss examples of plane curve singularities and explain the relation between exceptional collections of non-compact curves and distinguished collections of vanishing cycles.