Real Algebraic Geometry

Jacek Bochnak, Michel Coste, Marie-Françoise Roy

430 pages, parution le 01/01/1998

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Résumé

This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

Contents

Preface
Introduction 1

1 Ordered Fields, Real Closed Fields 7
2 Semi-algebraic Sets 23
3 Real Algebraic Varieties 59
4 Real Algebra 83
5 The Tarski-Seidenberg Principle as a Transfer Tool 97
6 Hilbert's 17th Problem. Quadratic Forms 103
7 Real Spectrum 133
8 Nash Functions 161
9 Stratifications 207
10 Real Places 245
11 Topology of Real Algebraic Varieties 263
12 Algebraic Vector Bundles 297
13 Polynomial or Regular Mappings with Values in Spheres 339
14 Algebraic Models of C[superscript [infinity]] Manifolds 373
15 Witt Rings in Real Algebraic Geometry 383

Bibliography 407
Index of Notation 421
Index 427

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jacek Bochnak, Michel Coste, Marie-Françoise Roy
Parution	01/01/1998
Nb. de pages	430
Format	16 x 24
Couverture	Relié
Poids	759g
Intérieur	Noir et Blanc
EAN13	9783540646631