Classification of Knots and Three-Dimensional Spaces

Classification of Knots and Three-Dimensional Spaces

by Geoffrey Hemion



Product Details

ISBN-13: 9780198596974
Publisher: Oxford University Press, USA
Publication date: 02/25/1993
Series: Oxford Science Publications
Pages: 168
Product dimensions: 6.44(w) x 9.56(h) x 0.58(d)

Table of Contents

1. Introduction
PART I: Preliminaries
2. What is a knot?
3. How to Compare Two Knots
4. The Theory of Compact Surfaces
5. Piecewise Linear Topology
PART II: The Theory of Normal Surfaces
6. Incompressible Surfaces
7. Normal Surfaces
8. Diophantine Inequalities
9. Fundamental Solutions
10. The "Easy" Case
11. The "Difficult" Case
12. Why is the "Difficult" Case Difficult?
13. What to do in the Difficult Case
PART III: Classifying Homeomorphisms of Surfaces
14. Straightening Homeomorphisms
15. The Conjugacy Problem
16. The Size of a Homeomorphism
17. Small Curves
18. Small Conjugating Homeomorphisms
19. Classifying Mappings of Surfaces
20. The Final Result

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