The Resource An Introduction to Knot Theory, by W.B.Raymond Lickorish, (electronic resource)

An Introduction to Knot Theory, by W.B.Raymond Lickorish, (electronic resource)

Label
An Introduction to Knot Theory
Title
An Introduction to Knot Theory
Statement of responsibility
by W.B.Raymond Lickorish
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
http://library.link/vocab/creatorName
Lickorish, W.B.Raymond
Dewey number
514/.224
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
x2D1IqOj3_I
Image bit depth
0
Language note
English
LC call number
  • QA613-613.8
  • QA613.6-613.66
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Graduate Texts in Mathematics,
Series volume
175
http://library.link/vocab/subjectName
  • Cell aggregation
  • Group theory
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Group Theory and Generalizations
  • Theoretical, Mathematical and Computational Physics
Label
An Introduction to Knot Theory, by W.B.Raymond Lickorish, (electronic resource)
Instantiates
Publication
Note
"With 114 Illustrations."
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
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
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (X, 204 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461268697
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0691-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089229
  • (SSID)ssj0000806845
  • (PQKBManifestationID)12426402
  • (PQKBTitleCode)TC0000806845
  • (PQKBWorkID)10750957
  • (PQKB)10460158
  • (SSID)ssj0001297217
  • (PQKBManifestationID)11858107
  • (PQKBTitleCode)TC0001297217
  • (PQKBWorkID)11363026
  • (PQKB)11527775
  • (DE-He213)978-1-4612-0691-0
  • (MiAaPQ)EBC3073377
  • (EXLCZ)993400000000089229
Label
An Introduction to Knot Theory, by W.B.Raymond Lickorish, (electronic resource)
Publication
Note
"With 114 Illustrations."
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
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
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (X, 204 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461268697
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0691-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089229
  • (SSID)ssj0000806845
  • (PQKBManifestationID)12426402
  • (PQKBTitleCode)TC0000806845
  • (PQKBWorkID)10750957
  • (PQKB)10460158
  • (SSID)ssj0001297217
  • (PQKBManifestationID)11858107
  • (PQKBTitleCode)TC0001297217
  • (PQKBWorkID)11363026
  • (PQKB)11527775
  • (DE-He213)978-1-4612-0691-0
  • (MiAaPQ)EBC3073377
  • (EXLCZ)993400000000089229

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