The Geometry of Four-Manifolds

Autore: Simon Kirwan Donaldson, S. K. Donaldson, P. B. Kronheimer

Codice: LISCMA0124202

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The Geometry of Four-Manifolds

Autore:

Codice: LISCMA0124202

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The Geometry of Four-Manifolds

Caratteristiche

Autore: 

Editore:  Clarendon Press

Luogo di stampa:  Oxford

Anno pubblicazione: 

Collana:  Oxford Mathematical Monographs

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.

Condizione prodotto:
Esemplare in buone condizioni. Copertina con tracce di polvere e segni d'usura. Ingiallimento delle pagine e tagli con tracce di polvere. Testo in inglese. Text in English. Book in good condition. Yellowed pages and edges with traces of dust. Yellowed cover/jacket with spots of dust and signs of use.

Codice ISBN:  0198502699

Codice EAN:  9780198502692

Pagine:  IX;440

Formato:  Brossura

Dimensioni (cm):
Altezza:  24
Larghezza:  16

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