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Knot theory
/* Put style overrides in here */
History of knot theory
Please e-mail suggestions of additional material to
a.ranicki@ed.ac.uk
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
BIBLIOGRAPHY OF P.G.TAIT
Provisional Bibliography
prepared by Chris Pritchard, July, 2001
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
BOOKS AND PAPERS
K.Reidemeister, Knotentheorie (Springer, 1932)
M.Epple, Die Enstehung der Knotentheorie, Vieweg (1999),
Mathematical review
J.Przytycki Little and Haseman -- early
American tabulators of knots
J.Przytycki Knot theory from Vandermonde to Jones.
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
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.
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