Real Algebraic Geometry / Edition 1

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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.

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Editorial Reviews

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"Wie schon das französische Original, so ist auch die englische Version sehr sorgfältig verfasst. Beim Vergleich zwischen beiden stösst man immer wieder auf Stellen, wo der ursprüngliche Text nicht nur einfach übersetzt, sondern im Interesse einer noch klareren Darstellung auch neu konzipiert worden ist. Kein Zweifel, dass die neue Fassung auch weiterhin die Rolle einer Standradreferenz spielen wird."
DMV Jahresbericht, 103. Band, Heft 2, Juli 2001
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Product Details

Table of Contents

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
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