We will discuss symplectic and contact manifolds, with a special emphasis on dimensions four and three. By results of Donaldson, Gompf and Giroux, the topological counterparts of these structures are Lefschetz fibrations and open book decompositions. In the study of these structures we need to examine mapping class group of surfaces (closed and with nonempty boundary).
The aim is to get a working knowledge of basic notions of symplectic and contact topology, and introduce the concepts of Lefschetz fibrations and open book decompositions. If time permits, we will also discuss Floer homologies.
Regular homework, and presentation or final
Topics in Algebra