ばいちょ(売価調査)、価格比較とネットでのお買い物を楽に

内容説明
This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology， and geometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years， and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that the fundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes， but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodular forms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central theme of this book is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds. One of the many consquences of this theory is that ’exotic’ smooth manifolds exist which are homeomorphic but not diffeomorphic to (4， and that large classes of forms cannot be realized as intersection forms whereas distinct manifolds may share the same form. These result have had far-reaching consequences in algebraic geometry， topology， and mathematical physics， and will continue to be a mainspring of mathematical research for years to come.
Book Description
The last ten years have seen rapid advances in the understanding of differentiable four-manifolds， not least of which has been the discovery of new ’exotic’ manifolds. These results have had far-reaching consequences in geometry， topology， and mathematical physics， and have proven to be a mainspring of current mathematical research. This book provides a lucid and accessible account of the modern study of the geometry of four-manifolds. Consequently， it will be required reading for all those mathematicians and theoretical physicists whose research touches on this topic. The authors present both a thorough treatment of the main lines of these developments in four-manifold topology--notably the definition of new invariants of four-manifolds--and also a wide-ranging treatment of relevant topics from geometry and global analysis. All of the main theorems about Yang-Mills instantons on four-manifolds are proven in detail. On the geometric side， the book contains a new proof of the classification of instantons on the four-sphere， together with an extensive discussion of the differential geometry of holomorphic vector bundles. At the end of the book the different strands of the theory are brought together in the proofs of results which settle long-standing problems in four-manifolds topology and which are close to the frontiers of current research. Co-author Donaldson is the 1994 co-recipient of the prestigious Crafoord Prize.