Knots and links

Author(s)

• Cromwell, Peter R.

Bibliographic Information

Knots and links

Peter R. Cromwell

Cambridge University Press, 2004

• : hbk.
• : pbk.

Note

Includes bibliographical references (p. 308-322) and index

Description and Table of Contents

Description

Knots and links are studied by mathematicians, and are also finding increasing application in chemistry and biology. Many naturally occurring questions are often simple to state, yet finding the answers may require ideas from the forefront of research. This readable and richly illustrated 2004 book explores selected topics in depth in a way that makes contemporary mathematics accessible to an undergraduate audience. It can be used for upper-division courses, and assumes only knowledge of basic algebra and elementary topology. Together with standard topics, the book explains: polygonal and smooth presentations; the surgery equivalence of surfaces; the behaviour of invariants under factorisation and the satellite construction; the arithmetic of Conway's rational tangles; arc presentations. Alongside the systematic development of the main theory, there are discussion sections that cover historical aspects, motivation, possible extensions, and applications. Many examples and exercises are included to show both the power and limitations of the techniques developed.

Table of Contents

• Preface
• 1. Introduction
• 2. A topologist's toolkit
• 3. Link diagrams
• 4. Constructions and decompositions of links
• 5. Spanning surfaces and genus
• 6. Matrix invariants
• 7. The Alexander-Conway polynomial
• 8. Rational tangles
• 9. More polynomials
• 10. Closed braids and arc presentations
• Appendix A. Knot diagrams
• Appendix B. Numerical invariants
• Appendix C. Properties
• Appendix D. Polynomials
• Appendix E. Polygon coordinates
• Appendix F. Family properties
• Bibliography
• Index.

by "Nielsen BookData"

Details

• NCID: BA69197700
• ISBN:
  • 0521839475
  • 0521548314
• LCCN: 2004045914
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xvii, 328 p.
• Size: 26 cm
• Classification:
  • LCC : QA612.2
  • DC22 : 514/.2242
• Subject Headings:
  • LCSH : Knot theory
  • LCSH : Link theory