Topology of Real Algebraic Sets

  • Selman Akbulut
  • Henry King

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 25)

Table of contents

  1. Front Matter
    Pages i-x
  2. Selman Akbulut, Henry King
    Pages 1-16
  3. Selman Akbulut, Henry King
    Pages 17-92
  4. Selman Akbulut, Henry King
    Pages 93-135
  5. Selman Akbulut, Henry King
    Pages 136-157
  6. Selman Akbulut, Henry King
    Pages 158-172
  7. Selman Akbulut, Henry King
    Pages 173-190
  8. Selman Akbulut, Henry King
    Pages 191-243
  9. Back Matter
    Pages 244-249

About this book

Introduction

In the Fall of 1975 we started a joint project with the ultimate goal of topo­ logically classifying real algebraic sets. This has been a long happy collaboration (c.f., [K2)). In 1985 while visiting M.S.R.1. we organized and presented our classification results up to that point in the M.S.R.1. preprint series [AK14] -[AK17]. Since these results are interdependent and require some prerequisites as well as familiarity with real algebraic geometry, we decided to make them self contained by presenting them as a part of a book in real algebraic geometry. Even though we have not arrived to our final goal yet we feel that it is time to introduce them in a self contained coherent version and demonstrate their use by giving some applications. Chapter I gives the overview of the classification program. Chapter II has all the necessary background for the rest of the book, which therefore can be used as a course in real algebraic geometry. It starts with the elementary properties of real algebraic sets and ends with the recent solution of the Nash Conjecture. Chapter III and Chapter IV develop the theory of resolution towers. Resolution towers are basic topologically defined objects generalizing the notion of manifold.

Keywords

Blowing up Dimension algebraic varieties homology topology

Authors and affiliations

  • Selman Akbulut
    • 1
  • Henry King
    • 2
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9739-7
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9741-0
  • Online ISBN 978-1-4613-9739-7
  • Series Print ISSN 0940-4740
  • About this book