An account is given of the compilation of the 1847319428 prime knots with 20 crossings.
Thistlethwaite, Morwen B  1
@article{10_2140_agt_2025_25_329,
author = {Thistlethwaite, Morwen B},
title = {The enumeration and classification of prime 20-crossing knots},
journal = {Algebraic and Geometric Topology},
pages = {329--344},
year = {2025},
volume = {25},
number = {1},
doi = {10.2140/agt.2025.25.329},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2025.25.329/}
}
TY - JOUR AU - Thistlethwaite, Morwen B TI - The enumeration and classification of prime 20-crossing knots JO - Algebraic and Geometric Topology PY - 2025 SP - 329 EP - 344 VL - 25 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2025.25.329/ DO - 10.2140/agt.2025.25.329 ID - 10_2140_agt_2025_25_329 ER -
Thistlethwaite, Morwen B. The enumeration and classification of prime 20-crossing knots. Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 329-344. doi: 10.2140/agt.2025.25.329
[1] , , New geometric splittings of classical knots and the classification and symmetries of arborescent knots, preprint (1979)
[2] , The next 350 million knots, from: "th International Symposium on Computational Geometry", Leibniz Int. Proc. Inform. 164, Schloss Dagstuhl (2020) 25 | DOI
[3] , , , , Regina, software for low-dimensional topology (1999–2023)
[4] , An enumeration of knots and links, and some of their algebraic properties, from: "Computational problems in abstract algebra", Pergamon (1970) 329 | DOI
[5] , Knots and links, Cambridge Univ. Press (2004) | DOI
[6] , , , , SnapPy, a computer program for studying the geometry and topology of 3-manifolds
[7] , Die beiden Kleeblattschlingen, Math. Ann. 75 (1914) 402 | DOI
[8] , , Classification of knot projections, Topology Appl. 16 (1983) 19 | DOI
[9] , , Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67
[10] , , A load balanced algorithm for the calculation of the polynomial knot and link invariants, from: "The mathematical heritage of C F Gauss", World Sci. (1991) 225 | DOI
[11] , A quick trip through knot theory, from: "Topology of -manifolds and related topics", Prentice-Hall (1961) 120
[12] , , Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 | DOI
[13] , Identifying noninvertible knots, Topology 22 (1983) 137 | DOI
[14] , , , The first 1,701,936 knots, Math. Intelligencer 20 (1998) 33 | DOI
[15] , The enumeration, description and construction of knots of fewer than ten crossings, Trans. Roy. Soc. Edinburgh 32 (1885) 281
[16] , Prime knots and tangles, Trans. Amer. Math. Soc. 267 (1981) 321 | DOI
[17] , On knots, with a census of order ten, Trans. Connecticut Acad. Sci. 18 (1885) 374
[18] , Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 | DOI
[19] , On the classification of knots, Proc. Amer. Math. Soc. 45 (1974) 262 | DOI
[20] , On dihedral covering spaces of knots, Invent. Math. 34 (1976) 77 | DOI
[21] , Analysis situs, J. École Polytech. 1 (1895) 1
[22] , , , Enumerating the prime alternating knots, I, J. Knot Theory Ramifications 13 (2004) 57 | DOI
[23] , Discrete parabolic representations of link groups, Mathematika 22 (1975) 141 | DOI
[24] , , The generalized tilt formula, Geom. Dedicata 55 (1995) 115 | DOI
[25] , Über die gruppen AaBb = 1, Abh. Math. Sem. Univ. Hamburg 3 (1924) 167 | DOI
[26] , Knoten und Vollringe, Acta Math. 90 (1953) 131 | DOI
[27] , , The rate of growth of the number of prime alternating links and tangles, Pacific J. Math. 182 (1998) 329 | DOI
[28] , On knots, I, Trans. Roy. Soc. Edinburgh 28 (1877) 145
[29] , On knots, II, Trans. Roy. Soc. Edinburgh 32 (1884) 327
[30] , On knots, III, Trans. Roy. Soc. Edinburgh 32 (1885) 493
[31] , On the structure and scarcity of alternating links and tangles, J. Knot Theory Ramifications 7 (1998) 981 | DOI
[32] , Non-invertible knots exist, Topology 2 (1963) 275 | DOI
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