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The classification of knots and 3-dimensional spaces

Author: Geoffrey Hemion
Publisher: Oxford ; New York : Oxford University Press, 1992.
Series: Oxford science publications.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Discusses the question of the classification of knots and arbitrary (compact) topological objects which occur in our normal space of physical reality. Professor Hemion explains his classification  Read more...

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Additional Physical Format: Online version:
Hemion, Geoffrey.
Classification of knots and 3-dimensional spaces.
Oxford ; New York : Oxford University Press, 1992
(OCoLC)622253093
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Geoffrey Hemion
ISBN: 0198596979 9780198596974
OCLC Number: 26128553
Description: 162 pages : illustrations ; 25 cm.
Contents: 1. Introduction --
pt. I. Preliminaries. 2. What is a knot? 3. How to compare two knots. 4. The theory of compact surfaces. 5. Piecewise linear topology --
pt. 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 --
pt. III. Classifying Homeomorphisms of Surfaces. 14. Straightening homeomorphisms. 15. The conjugacy problem. 16. The hyperbolic plane. 17. Movements of the hyperbolic plane. 18. The size of a homeomorphism. 19. Small curves. 20. Small conjugating homeomorphisms. 21. Classifying mappings of surfaces. 22. The final result --
A. Homeomorphisms of surfaces. A.1. Isotopies of f, g, and h. A.1.1. Some preliminary results and definitions. A.1.2. The definition of the fundamental region. A.1.3. The size of a homeomorphism. A.1.4. New choices for f, g, and h. A.1.5. The elimination of trivial intersections. A.1.6. Straightening the homeomorphisms. A.1.7. Agreement between [actual symbol not reproducible] and [actual symbol not reproducible] on [actual symbol not reproducible]. A.1.8. Agreement between [actual symbol not reproducible] and [actual symbol not reproducible] everywhere. A.2. The small curve, c. A.2.1. The definition of the arcs [actual symbol not reproducible]. A.2.2. The basic idea for constructing c. A.2.3. The 'link' of B and the definition of a particular case. A.2.4. The points z[subscript i]. A.2.5. Non-parallelity regions in the fundamental regions. A.2.6. Constructing the curve c in our special case. A.2.7. Proving that c is not deformable to a boundary in our special case. A.2.8. The second special case: 'many' [actual symbol not reproducible] pass through [sigma]. A.2.9. The third, and last, special case: all [actual symbol not reproducible] pass through [sigma]. A.3. Solution of conjugacy problem. A.3.1. Estimating the size of h. A.3.2. The generalization to surfaces without boundary. A.3.3. The proof of the conjugacy theorem.
Series Title: Oxford science publications.
Other Titles: Classification of knots and three-dimensional spaces.
Responsibility: Geoffrey Hemion.
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an informal account of Haken's classification of sufficiently large 3-manifolds by means of normal surfaces ... appropriate for someone who wants a broad overview of this theorem in 3-dimensional Read more...

 
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