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This volume is an introduction to Knot Theory. It includes a selection of topics which graduate students have found to be a successful introduction to the field and employs three distinct techniques; Algebraic Topology, Combinatorics, and Algebraic Topology. Each topic is developed until a significant result is achieved and chapters end with exercises and brief accounts of state-of-the-art research.
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Recensione
W.B.R. Lickorish
An Introduction to Knot Theory
"This essential introduction to vital areas of mathematics with connections to physics, while intended for graduate students, should fall within the ken of motivated upper-division undergraduates."―CHOICE
Contenuti
1. A Beginning for Knot Theory.- Exercises.- 2. Seifert Surfaces and Knot Factorisation.- Exercises.- 3. The Jones Polynomial.- Exercises.- 4. Geometry of Alternating Links.- Exercises.- 5. The Jones Polynomial of an Alternating Link.- Exercises.- 6. The Alexander Polynomial.- Exercises.- 7. Covering Spaces.- Exercises.- 8. The Conway Polynomial, Signatures and Slice Knots.- Exercises.- 9. Cyclic Branched Covers and the Goeritz Matrix.- Exercises.- 10. The Arf Invariant and the Jones Polynomia.- Exercises.- 11. The Fundamental Group.- Exercises.- 12. Obtaining 3-Manifolds by Surgery on S3.- Exercises.- 13. 3-Manifold Invariants From The Jones Polynomial.- Exercises.- 14. Methods for Calculating Quantum Invariants.- Exercises.- 15. Generalisations of the Jones Polynomial.- Exercises.- 16. Exploring the HOMFLY and Kauffman Polynomials.- Exercises.- References.
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An Introduction to Knot Theory
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. * Written by an internationally acknowledged expert in the field who has won prizes for both exposition and research * Gives a comprehensive introduction to the field, presenting modern developments in the context of classical material * Will appeal to grad. Codice articolo 4189506
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An Introduction to Knot Theory
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Springer New York Okt 2012, 2012
ISBN 10: 1461268699
ISBN 13: 9781461268697
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area. 220 pp. Englisch. Codice articolo 9781461268697
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An Introduction to Knot Theory
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Springer New York, Springer New York Okt 2012, 2012
ISBN 10: 1461268699
ISBN 13: 9781461268697
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Taschenbuch
Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Taschenbuch. Condizione: Neu. Neuware -This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 220 pp. Englisch. Codice articolo 9781461268697
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An Introduction to Knot Theory (Graduate Texts in Mathematics)
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Condizione: New. In English. Codice articolo ria9781461268697_new
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An Introduction to Knot Theory
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Springer New York, Springer New York, 2012
ISBN 10: 1461268699
ISBN 13: 9781461268697
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Da: AHA-BUCH GmbH, Einbeck, Germania
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory. Codice articolo 9781461268697
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Introduction to Knot Theory
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An Introduction to Knot Theory
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An Introduction to Knot Theory
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An Introduction to Knot Theory
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ISBN 10: 1461268699
ISBN 13: 9781461268697
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Paperback / softback. Condizione: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 373. Codice articolo C9781461268697
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Introduction to Knot Theory
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