Spin c Structures on 3- and 4-Manifolds

Spinc structures turn out to be very useful tools in understanding homotopic properties of contact structures. In addition, gauge theoretic invariants — such as Seiberg-Witten and Ozsváth-Szabó invariants — are defined for spinc 3- and 4-manifolds. This chapter is devoted to the review of spinc structures — with a special emphasis on the 3- and 4-dimensional case. Throughout this chapter we will assume that the reader is familiar with the basics of the theory of characteristic classes. (For an excellent reference see [116].) For a more complete treatment of spine structures the reader is advised to turn to [113].