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The Classification of Knots and 3-Dimensional Spaces by Geoffrey Hemion (Professor of Mathematics, Professor of Mathematics, University of Bielefeld) at Abbey's Bookshop,
The Classification of Knots and 3-Dimensional Spaces
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Geoffrey Hemion (Professor of Mathematics, Professor of Mathematics, University of Bielefeld)

The Classification of Knots and 3-Dimensional Spaces

Geoffrey Hemion (Professor of Mathematics, Professor of Mathematics, University of Bielefeld)

$242

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English
Oxford University Press
07 January 1993
Algebraic topology; Analytic topology; Scientific nomenclature & classification
People have been interested in knots at least since the time of Alexander the Great and his encounter with the Gordian knot. There are famous knot illustrations in the Book of Kells and throughout traditional Islamic art. Lord Kelvin believed that atoms were knots in the ether and he encouraged Tait to compile a talbe of knots about 100 years ago. In recent years, the Jones polynomial has stimulated much interest in possible relationships between knot theory and physics. The book is concerned with the fundamental question of the classification of knots, and more generally the classification of arbitrary (compact) topological objects which can occur in our normal space of physical reality. Professor Hemion explains his classification algorithm - using the method of normal surfaces - in a simple and concise way. The reader is thus shown the relevance of such traditional mathematical objects as the Klein bottle or the hyperbolic plane to this basic classification theory. The Classification of Knots and 3-dimensional Spaces will be of interest to mathematicians, physicists, and other scientists who want to apply this basic classification algorithm to their research in knot theory.
By:  
Imprint:   Oxford University Press
Country of Publication:   United Kingdom
Dimensions:   Height: 235mm,  Width: 162mm,  Spine: 16mm
Weight:   386g
ISBN:   9780198596974
ISBN 10:   0198596979
Pages:   168
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Professional & Vocational ,  A / AS level ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active
"Introduction Part I: Preliminaries 1: What is a knot? 2: How to compare two knots 3: The theory of compact surfaces 4: Piecewise linear topology Part II: The Theory of Normal Surfaces 5: Incompressible surfaces 6: Normal surfaces 7: Diophantine inequalities 8: Fundamental solutions 9: The ""easy"" case 10: The ""difficult"" case 11: Why is the ""difficult"" case difficult? 12: What to do in the difficult case Part III: Classifying Homeomorphisms of Surfaces 13: Straightening homeomorphisms 14: The conjugacy problem 15: The size of a homeomorphism 16: Small curves 17: Small conjugating homeomorphisms 18: Classifying mappings of surfaces 19: The final result"

Reviews for The Classification of Knots and 3-Dimensional Spaces

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 topology Martin Scharlemann, Mathematical Reviews, Issue 94g


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