The Topology of Knots

  • Martin Gardner

Abstract

To a topologist knots are closed curves embedded in three-dimensional space. It is useful to model them with rope or cord and to diagram them as projections on a plane. If it is possible to manipulate a closed curve—of course, it must not be allowed to pass through itself— so that it can be projected on a plane as a curve with no crossing points, then the knot is called trivial. In ordinary discourse one would say the curve is not knotted. “Links” are two or more closed curves that cannot be separated without passing one through another.

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References

Books

  1. Introduction to Knot Theory. R. H. Crowell and R. H. Fox. Blaisdell, 1963; Springer-Verlag, 1977.Google Scholar
  2. Knots and Links. Dale Rolfsen. Publish or Perish, 1976, Second edition, 1990.Google Scholar
  3. On Knots. Louis Kauffman. Princeton University Press, 1987.MATHGoogle Scholar
  4. New Developments in the Theory of Knots. Toshitake Kohno. World Scientific, 1990.MATHCrossRefGoogle Scholar
  5. The Geometry and Physics of Knots. Michael Ativan. Cambridge University Press, 1990.Google Scholar
  6. Knots and Physics. Louis Kauffman. World Scientific, 1991.MATHGoogle Scholar
  7. Knot Theory. Charles Livingston. Mathematical Association of America, 1993.MATHGoogle Scholar
  8. The Knot Book. Colin C. Adams. Freeman, 1994.MATHGoogle Scholar
  9. The History and Science of Knots. J. C. Turner and P. van de Griend. World Scientific, 1996.Google Scholar

Papers

  1. Out of hundreds of papers on knot theory published since 1980, I have selected only a few that have appeared since 1990.Google Scholar
  2. Untangling DNA. De Witt Summers in The Mathematical Intelligencer ,Vol. 12, pages 71–80; 1990.CrossRefMathSciNetGoogle Scholar
  3. Knot Theory and Statistical Mechanics. Vaughan F. R. Jones, in Scientific American ,pages 98–103; November 1990.Google Scholar
  4. Recent Developments in Braid and Link Theory. Joan S. Birman in The Mathematical Intelligencer ,Vol. 13, pages 57–60; 1991.CrossRefMathSciNetGoogle Scholar
  5. Knotty Problems—and Real-World Solutions. Barry Cipra in Science ,Vol. 255, pages 403–404; January 24, 1992.CrossRefGoogle Scholar
  6. Knotty Views. Ivars Peterson in Science News ,Vol. 141, pages 186–187; March 21, 1992.CrossRefGoogle Scholar
  7. Knots, Links and Videotape. Ian Stewart in Scientific American ,pages 152– 154; January 1994.Google Scholar
  8. Braids and Knots. Alexey Sosinsky in Quantum ,pages 11–15; January/ February 1995.Google Scholar
  9. How Hard Is It to Untie a Knot? William Menasco and Lee Rudolph in American Scientist ,Vol. 83, pages 38–50; January/February 1995.Google Scholar
  10. The Color Invariant for Knots and Links. Peter Andersson in American Mathematical Monthly ,Vol. 102, pages 442–448; May 1995.MATHCrossRefMathSciNetGoogle Scholar
  11. Geometry and Physics. Michael Atiyah in The Mathematical Gazette ,pages 78–82; March 1996.Google Scholar
  12. Knots Landing. Robert Matthews in New Scientist ,pages 42–43; February 1, 1997.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Martin Gardner

There are no affiliations available

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