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Cover: 9780387982540 | An Introduction to Knot Theory | W. B. Raymond Lickorish | Buch | x
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An Introduction to Knot Theory
Buch von W. B. Raymond Lickorish
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1997
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: x
204 S.
ISBN-13: 9780387982540
ISBN-10: 038798254X
Sprache: Englisch
Herstellernummer: 10628672
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lickorish, W. B. Raymond
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 18 mm
Von/Mit: W. B. Raymond Lickorish
Erscheinungsdatum: 03.10.1997
Gewicht: 0,5 kg
Artikel-ID: 106830244
Zusammenfassung
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1997
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: x
204 S.
ISBN-13: 9780387982540
ISBN-10: 038798254X
Sprache: Englisch
Herstellernummer: 10628672
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lickorish, W. B. Raymond
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 18 mm
Von/Mit: W. B. Raymond Lickorish
Erscheinungsdatum: 03.10.1997
Gewicht: 0,5 kg
Artikel-ID: 106830244
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