Fillings of Contact 3-Manifolds

This chapter is devoted to the study of fillability properties of contact 3-manifolds. After having the necessary definitions we will see different types of fillings, and give a family of tight, nonfillable contact structures. The construction of these latter examples utilizes contact surgery, while tightness is proved by computing contact Ozsváth-Szabó invariants (see Chapter 14). In the last section we will concentrate on topological restrictions a contact 3-manifold imposes on its Stein fillings.