The Geometry of Four-Manifolds
Caractéristiques
Auteur: Simon Kirwan Donaldson, S. K. Donaldson, P. B. Kronheimer
Éditeur: Clarendon Press
Lieu d'impression: Oxford
Année de publication: 2010
Collier: Monographies mathématiques d'Oxford
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, andgeometry 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 thefundamental 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 unimodularforms 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 connectionsover 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 havehad far-reaching consequences in algebraic geometry, topology, and mathematical physics, and will continue to be a mainspring of mathematical research for years to come.
État du produit:
Spécimen en bon état. Couvrir avec des traces de poussière et des signes d'usure. Jaunissement des pages et coupures avec traces de poussière. Texte en anglais. Texte en anglais. Livre en bon état. Pages et bords jaunis avec traces de poussière. Couverture/jaune jauni avec des taches de poussière et des signes d'utilisation.
Code ISBN: 0198502699
EAN: 9780198502692
Pages: IX ; 440
Format: Broché
Dimensions (cm):
Hauteur: 24
Largeur: 16
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