The Topology of Knots
- Martin Gardner
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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.
- Introduction to Knot Theory. R. H. Crowell and R. H. Fox. Blaisdell, 1963; Springer-Verlag, 1977.
- Knots and Links. Dale Rolfsen. Publish or Perish, 1976, Second edition, 1990.
- On Knots. Louis Kauffman. Princeton University Press, 1987.
- New Developments in the Theory of Knots. Toshitake Kohno. World Scientific, 1990. CrossRef
- The Geometry and Physics of Knots. Michael Ativan. Cambridge University Press, 1990.
- Knots and Physics. Louis Kauffman. World Scientific, 1991.
- Knot Theory. Charles Livingston. Mathematical Association of America, 1993.
- The Knot Book. Colin C. Adams. Freeman, 1994.
- The History and Science of Knots. J. C. Turner and P. van de Griend. World Scientific, 1996.
- Out of hundreds of papers on knot theory published since 1980, I have selected only a few that have appeared since 1990.
- Untangling DNA. De Witt Summers in The Mathematical Intelligencer ,Vol. 12, pages 71–80; 1990. CrossRef
- Knot Theory and Statistical Mechanics. Vaughan F. R. Jones, in Scientific American ,pages 98–103; November 1990.
- Recent Developments in Braid and Link Theory. Joan S. Birman in The Mathematical Intelligencer ,Vol. 13, pages 57–60; 1991. CrossRef
- Knotty Problems—and Real-World Solutions. Barry Cipra in Science ,Vol. 255, pages 403–404; January 24, 1992. CrossRef
- Knotty Views. Ivars Peterson in Science News ,Vol. 141, pages 186–187; March 21, 1992. CrossRef
- Knots, Links and Videotape. Ian Stewart in Scientific American ,pages 152– 154; January 1994.
- Braids and Knots. Alexey Sosinsky in Quantum ,pages 11–15; January/ February 1995.
- How Hard Is It to Untie a Knot? William Menasco and Lee Rudolph in American Scientist ,Vol. 83, pages 38–50; January/February 1995.
- The Color Invariant for Knots and Links. Peter Andersson in American Mathematical Monthly ,Vol. 102, pages 442–448; May 1995. CrossRef
- Geometry and Physics. Michael Atiyah in The Mathematical Gazette ,pages 78–82; March 1996.
- Knots Landing. Robert Matthews in New Scientist ,pages 42–43; February 1, 1997.
- The Topology of Knots
- Book Title
- The Last Recreations
- Book Subtitle
- Hydras, Eggs, and Other Mathematical Mystifications
- pp 67-84
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- Springer New York
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- Springer-Verlag New York
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