Lectures on Seiberg-Witten Invariants

In October 1994 Seiberg-Witten invariants entered in 4-manifold theory with a big bang. Not only did these invariants tidy up the Gauge Theory, but they also gave some exciting new results on topology of smooth 4-manifolds. These notes grew out of the lectures I have given in learning seminars at MPI in Bonn, and METU in Ankara on this subject. The main goal of these notes is not to survey the whole area, but rather establish conventions for novice topologist like myself, and go through some recent selected results. In these notes I avoided the general Clifford algebra constructions in favor of more direct representation theory of Spinc(4). I have benefited greatly from stimulating papers [KM], [W], and [T], as well as unpublished lecture notes of C.Taubes. I also benefited seminar talks by R.Fintushel, D.Salamon, T.Parker and T.Draghici. I thank I.Hambelton and T.Onder for inviting me to MPI and METU, giving me the chance to work on these notes. I make no claim of originality in these notes, they are merely modest efforts to understand the results from the sources mentioned above.