Topology of Real Algebraic Sets

1. Front Matter

   Pages i-x

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2. Introduction

   • Selman Akbulut, Henry King

   Pages 1-16

3. Algebraic Sets

   • Selman Akbulut, Henry King

   Pages 17-92

4. Ticos

   • Selman Akbulut, Henry King

   Pages 93-135

5. Resolution Towers

   • Selman Akbulut, Henry King

   Pages 136-157

6. Algebraic Structures on Resolution Towers

   • Selman Akbulut, Henry King

   Pages 158-172

7. Resolution Tower Structures on Algebraic Sets

   • Selman Akbulut, Henry King

   Pages 173-190

8. The Characterization of Three Dimensional Algebraic Sets

   • Selman Akbulut, Henry King

   Pages 191-243

9. Back Matter

   Pages 244-249

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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.

• Blowing up
• Dimension
• algebraic varieties
• homology
• topology

• Department of Mathematics, Michigan State University, East Lansing, USA

  Selman Akbulut

• Department of Mathematics, University of Maryland, College Park, USA

  Henry King

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