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OverviewPeople 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. Full Product DetailsAuthor: Geoffrey Hemion (Professor of Mathematics, Professor of Mathematics, University of Bielefeld)Publisher: Oxford University Press Imprint: Oxford University Press Dimensions: Width: 16.20cm , Height: 1.60cm , Length: 23.50cm Weight: 0.386kg ISBN: 9780198596974ISBN 10: 0198596979 Pages: 168 Publication Date: 07 January 1993 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsIntroduction 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 resultReviewsan 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 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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