Many techniques for studying symplectic manifolds (e.g. Gromov-Witten invariants) rely on the ability to count certain pseudoholomorphic curves. In order to do this counting one must have some notion of fundamental class on the moduli space of pseudoholomorphic curves. However, such moduli spaces are generally very poorly behaved. In this talk, we will discuss Kuranishi spaces which are a geometric structure one can equip these moduli spaces with in order to define a virtual fundamental class.
Kuranishi Space