Knot theory

Please e-mail suggestions of additional material to a.ranicki@ed.ac.uk

An online archive of source material on knots.

A small personal selection from the 10,000+ items in the Mathematical Reviews which include "knot" in the review.
Geared to high-dimensional knots and knot cobordism.

BIOGRAPHIES OF EARLY KNOT THEORISTS

Links to biographical entries in the MacTutor St. Andrews Mathematics History Archive.
  • M.Dehn
  • P.Heegaard. Heegaard's thesis (1898). See also the Heegaard home page.
  • T.P.Kirkman
  • J.B.Listing
  • F.Meyer
  • K.Reidemeister
  • O.Schreier
  • P.G.Tait
  • W.Thomson (Lord Kelvin)
  • W.Wirtinger

    • P.G.TAIT

  • P.G.Tait (MacTutor entry)
  • Biography by C.G.Knott
  • Scienific Papers, Vol. 1
  • Scienific Papers, Vol. 2
  • Bibliography prepared by Chris Pritchard and David Forfar.

    • EARLY PAPERS ON KNOT THEORY

  • J.B.Listing, Vorstudien zur Topologie, Goettinger Studien (Abtheilung 1) 1 (1847), 811-875
  • A.Cayley, On a problem of arrangements, Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 338-342
  • Crum Brown, On a case of interlacing surfaces, Proc. Royal Soc. Edinburgh, Vol. 13, 121 (1885-6), 382-386
  • M.G.Haseman On knots, with a census of the amphicheirals with twelve crossings Trans. Roy. Soc. Edinburgh, 52 (1917-8), 235-255
    also Ph.D thesis, Bryn Mawr College, 1918
    printed by Neill & Co. limited, 212 Causewayside, Edinburgh - 1918.
  • M.G.Haseman Amphicheiral knots Trans. Roy. Soc. Edinburgh 52 (1919-20), 597-602.
  • P.Heegaard Forstudier til en topologisk teori for de algebraiske fladers sammehaeng Thesis (in Danish, Nordiske Forlag, Copemhagen, 1898), Sur l'Analysis situs (French translation, Bulletin de la S.M.F. 44, 161-242 (1916))
  • T.P.Kirkman The enumeration, description, and construction of knots of fewer than 10 crossings Trans. Roy. Soc. Edinburgh 32 (1883-4), 281-309.
  • T.P.Kirkman The 364 unifilar knots of ten crossings, enumerated and described Trans. Roy. Soc. Edinburgh 32 (1884-5), 483-491. Two appendices in Proc. Roy. Soc. Edinburgh 13, p. 359.
  • T.P.Kirkman Examples upon the Reading of the Circle or Circles of a Knot Proc. Royal Soc. Edinburgh, Vol. ?? (1885-6), 693-698
  • T.P.Kirkman On the twists of Listing and Tait Proc. Royal Soc. Edinburgh, Vol. 13, 120 (1884-5), 363-367
  • T.P.Kirkman Demonstration of Theorems A,B,C etc. Proc. Royal Soc. Edinburgh, Vol. 13, 120 (1884-5), 359-363
  • T.P.Kirkman, On the linear section PR of a knot M_n, which passes through two crossings P and R, which meets no edge, and which cuts away a (3+r)-gonal mesh of M_n, Proc. Royal Soc. Edinburgh, Vol. 13, 121 (1884-5), 514-522
  • C.N.Little, On knots, with a census for order 10, Trans. Connecticut Academy Sci. 18, Vol. 7 (1885), 27-43 (1-17 ??).
  • C.N.Little, Non-Alternate knots of order eight and nine, Trans. Royal. Soc. Edinburgh 35, 1890
  • C.N.Little Alternate +/-Knots of order eleven Trans. Royal. Soc. Edinburgh 36 (1890-1), 253-255.
  • C.N.Little, Non-Alternate +/-Knots, Trans. Royal. Soc. Edinburgh 39 (1898-9), 771-778.
  • F.Meyer Ueber algebraische Knoten Proc. Royal Soc. Edinburgh, Vol. 13, 97 (1885-6), 931-946
  • P.G.Tait, Some elementary properties of closed plane curves, Messenger of Mathematics, New Series, No.69, 1877, (communicated at the 1876 Meeting of the British Association).
  • P.G.Tait, On knots, Proc. Royal Soc. Edinburgh, Vol. 9, 97 (1876-7), 306-317
  • P.G.Tait, On links, Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 321-332
  • P.G.Tait, Sevenfold knottiness, Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 363-366
  • P.G.Tait Applications of the theorem that two closed plane curves intersect an even number of times Proc. Royal Soc. Edinburgh, Vol. 9, 97 (1876-7), 237-246
  • P.G.Tait Note on the measure of beknottedness Proc. Royal Soc. Edinburgh, Vol. 9, 97 (1876-7), 289-298
  • P.G.Tait On amphicheiral forms and their relations Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 391-392
  • P.G.Tait Preliminary note on a new method of investigating the properties of knots Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 403
  • P.G.Tait Additional remarks on knots Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 405
  • P.G.Tait On knots I. Trans. Roy. Soc. Edinburgh 28 (1876-7), 145-190
  • P.G.Tait On knots II. Trans. Roy. Soc. Edinburgh 32 (1883-4), 327-342
  • P.G.Tait On knots III. Trans. Roy. Soc. Edinburgh 32 (1884-5),493-506
  • P.G.Tait, Johann Benedict Listing, Nature 27 (1882-83), 316.
  • P.G.Tait, Listing's Topologie (Introductory address to the Edinburgh Mathematical Society, November 9, 1883), Philosophical Magazine, January, 1884.
  • W.Thomson Vortex statics Proc. Royal Soc. Edinburgh Vol. 9, 94 (1875-6), 59-73
  • H.Brunn Ueber Verkettung Sitzungsber. Bayr. Akad. 22, 77-99 (1892)

    • BOOKS AND PAPERS ABOUT THE HISTORY OF KNOT THEORY

  • M.Epple, Die Enstehung der Knotentheorie, Vieweg (1999), Mathematical review
  • J.Przytycki Little and Haseman -- early American tabulators of knots
  • J.Przytycki The classical roots of knot theory. Chaos, Solitons and Fractals 9, 531--545 (1998)

    • THE ORIGINAL PAPERS ON THE ALEXANDER POLYNOMIAL, SEIFERT SURFACES AND MATRICES, CONWAY'S ENUMERATION OF KNOTS AND LINKS

  • Topological invariants of knots and links by J.W.Alexander, Transactions of A.M.S. 30, 275--306 (1928)
  • Ein Knotensatz mit Anwendung auf Dimensionstheorie by P.Frankl and L.Pontrjagin, Math. Ann. 102, 785--789 (1930)
  • Ueber das Geschlecht von Knoten by H.Seifert, Math. Ann. 110, 571--592 (1934)
  • An enumeration of knots and links, and some of their algebraic properties by J.H.Conway, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967), 329--358, Pergamon (1970)

    • SOME KNOT WEBSITES

  • A Bibliography of Literature on Knots and Braids by Joyce Rile (1991).
  • Knot Atlas (wiki)
  • SeifertView Windows programme for the visualisation of knots and links, and their Seifert surfaces. Try the roller coaster ride! (misc, esc for full screen)
  • Knotilus
  • KnotPlot
  • Knots worth knowing
  • The hagfish (Thanks to John Murray for the weblink).
  • Julia Collins.