Interactions of symplectic topology with singularity theory: Lagrangian pinwheels, Klein bottles and Milnor links of singularities

Abstract

In this thesis we examine certain phenomena in symplectic topology which are related to the theory of isolated singularities. The biggest part of the thesis is devoted to rigidity properties of Lagrangian pinwheels, which are vanishing cycles of certain quotient singularities. In another direction, we study how different isolated hypersurface singularities give rise to exotic contact structures.