Floer Homology Groups in Yang-Mills Theory [Hardcover]

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.This monograph aims to give a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The techniques used here are now known to be important for many current areas of research. The author writes with the big picture constantly in mind, reviewing the current state of knowledge and predicting the likely direction of future research. The results described form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution.This monograph aims to give a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The techniques used here are now known to be important for many current areas of research. The author writes with the big picture constantly in mind, reviewing the current state of knowledge and predicting the likely direction of future research. The results described form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution.This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for self-dual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated Seiberg-Witten invariants. The results described in this volume form part of the area known as Donaldson theorl3$