2023
Morton, H. (2023). Tangles in affine Hecke algebras. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. doi:10.1142/S0218216523400187DOI: 10.1142/S0218216523400187
2022
2021
Morton, H., & Samuelson, P. (2021). DAHAs and skein theory. Communications in Mathematical Physics. Retrieved from http://arxiv.org/abs/1909.11247v2
2020
Morton, H. (2020). Satellites and quantum invariants. In C. Adams, E. Flapan, L. Kauffman, A. Heinrich, L. Ludwig, & S. Nelson (Eds.), Encyclopedia of Knot Theory. CRC Press.
2019
2015
Morton, H. R. (2015). Mutant Knots. In NEW IDEAS IN LOW DIMENSIONAL TOPOLOGY (Vol. 56, pp. 379-412). Retrieved from https://www.webofscience.com/
2014
Morton, H., & Samuelson, P. (2017). THE HOMFLYPT SKEIN ALGEBRA OF THE TORUS AND THE ELLIPTIC HALL ALGEBRA. DUKE MATHEMATICAL JOURNAL, 166(5), 801-854. doi:10.1215/00127094-3718881DOI: 10.1215/00127094-3718881
2011
KNOTS, SATELLITES AND QUANTUM GROUPS (Chapter)
Morton, H. R. (2011). KNOTS, SATELLITES AND QUANTUM GROUPS. In Introductory Lectures on Knot Theory (pp. 379-406). WORLD SCIENTIFIC. doi:10.1142/9789814313001_0014DOI: 10.1142/9789814313001_0014
2010
Morton, H. R. (2010). A basis for the Birman-Wenzl algebra. Retrieved from http://arxiv.org/abs/1012.3116v1
Garoufalidis, S., Morton, H., & Thao, V. (2013). THE SL<sub>3</sub> COLORED JONES POLYNOMIAL OF THE TREFOIL. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 141(6), 2209-2220. doi:10.1090/S0002-9939-2013-11582-0DOI: 10.1090/S0002-9939-2013-11582-0
2009
Morton, H. R., & Ryder, N. D. A. (2010). Relations between Kauffman and Homfly satellite invariants. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 149, 105-114. doi:10.1017/S0305004110000058DOI: 10.1017/S0305004110000058
2008
Morton, H. R., & Grishanov, S. (2009). DOUBLY PERIODIC TEXTILE STRUCTURES. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 18(12), 1597-1622. doi:10.1142/S0218216509007646DOI: 10.1142/S0218216509007646
2007
Morton, H. R., & Ryder, N. (2009). INVARIANTS OF GENUS 2 MUTANTS. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 18(10), 1423-1438. doi:10.1142/S0218216509007506DOI: 10.1142/S0218216509007506
Morton, H. R., & Manchon, P. M. G. (2008). Geometrical relations and plethysms in the Homfly skein of the annulus. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 78, 305-328. doi:10.1112/jlms/jdn026DOI: 10.1112/jlms/jdn026
Morton, H. R. (2009). Mutant knots with symmetry. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 146, 95-107. doi:10.1017/S0305004108001862DOI: 10.1017/S0305004108001862
2006
Morton, H. R. (2006). The Alexander polynomial of a torus knot with twists. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 15(8), 1037-1047. doi:10.1142/S0218216506004920DOI: 10.1142/S0218216506004920
Morton, H. R. (2007). Integrality of Homfly 1-tangle invariants. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 7, 327-338. doi:10.2140/agt.2007.7.327DOI: 10.2140/agt.2007.7.327
Morton, H. R. (2006). Murphy operators in Knot Theory. In Unknown Book (Vol. 10, pp. 359-366). doi:10.1142/9789812772527_0031DOI: 10.1142/9789812772527_0031
2004
Hadji, R. J., & Morton, H. R. (2006). A basis for the full Homfly skein of the annulus. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 141, 81-100. doi:10.1017/S0305004105009047DOI: 10.1017/S0305004105009047
2003
Morton, H. R., & Hadji, R. J. (2005). Conjugacy for positive permutation braids. FUNDAMENTA MATHEMATICAE, 188, 155-166. doi:10.4064/fm188-0-8DOI: 10.4064/fm188-0-8
2001
Morton, H. R. (2001). Power sums and Homfly skein theory. Geom. Topol. Monogr., 4, 235-244. Retrieved from http://arxiv.org/abs/math/0111101v3
Morton, H. R., & Lukac, S. G. (2003). The Homfly polynomial of the decorated Hopf link. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 12(3), 395-416. doi:10.1142/S0218216503002536DOI: 10.1142/S0218216503002536
Morton, H. R., & Hadji, R. J. (2001). Homfly Polynomials of Generalized Hopf Links. Algebr. Geom. Topol., 2, 11-32. Retrieved from http://dx.doi.org/10.2140/agt.2002.2.11DOI: 10.2140/agt.2002.2.11
Morton, H. R. (2002). Skein theory and the Murphy operators. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 11(4), 475-492. doi:10.1142/S0218216502001767DOI: 10.1142/S0218216502001767
2000
The spread and extreme terms of Jones polynomials (Journal article)
Bae, Y., & Morton, H. R. (2003). The spread and extreme terms of Jones polynomials. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 12(3), 359-373. doi:10.1142/S0218216503002512DOI: 10.1142/S0218216503002512
MUTUAL BRAIDING AND THE BAND PRESENTATION OF BRAID GROUPS (Conference Paper)
MORTON, H. R., & RAMPICHINI, M. (2000). MUTUAL BRAIDING AND THE BAND PRESENTATION OF BRAID GROUPS. In Knots in Hellas '98. WORLD SCIENTIFIC. doi:10.1142/9789812792679_0020DOI: 10.1142/9789812792679_0020
1999
Morton, H. R., & Rampichini, M. (1999). Mutual braiding and the band presentation of braid groups. Retrieved from http://arxiv.org/abs/math/9907017v1
Morton, H., & Hodgson, J. (1999). Multiburau [Computer Software].
1998
Morton, H. R., & Ryder, H. J. (1998). Mutants and SU(3)_q invariants. Retrieved from http://arxiv.org/abs/math/9810197v1
Morton, H. R. (1998). The Multivariable Alexander Polynomial for a Closed Braid. Retrieved from http://arxiv.org/abs/math/9803138v1
Morton, H. R. (1999). The Burau matrix and Fiedler's invariant for a closed braid. TOPOLOGY AND ITS APPLICATIONS, 95(3), 251-256. doi:10.1016/S0166-8641(98)00009-1DOI: 10.1016/S0166-8641(98)00009-1
MORTON, H. R., & BELTRAMI, E. (1998). Arc index and the Kauffman polynomial. Mathematical Proceedings of the Cambridge Philosophical Society, 123(1), 41-48. doi:10.1017/s0305004197002090DOI: 10.1017/s0305004197002090
1997
Idempotents of Hecke algebras of type A. (Journal article)
Aiston, A. K., & Morton, H. R. (1998). Idempotents of Hecke algebras of type A.. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 7(4), 463-487. doi:10.1142/S0218216598000243DOI: 10.1142/S0218216598000243
Morton, H. R., & Aiston, A. K. (1997). Young diagrams, the Homfly skein of the annulus and unitary invariants. In S. Suzuki (Ed.), Knots '96 (pp. 31-45). Singapore: World Scientific.
1996
Morton, H. R., & Cromwell, P. R. (1996). Distinguishing mutants by knot polynomials. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 5(2), 225-238. doi:10.1142/S0218216596000163DOI: 10.1142/S0218216596000163
Morton, H. R. (1996). Unitary quantum groups and mutant knots. In M. -L. Ge, & F. Wu (Eds.), Statistical Models, Yang-Baxter Equation and related Topics (pp. 254-261). Singapore: World Scientific.
1995
Morton, H. R. (1995). Fibonacci-like Sequences and Greatest Common Divisors. The American Mathematical Monthly, 102(8), 731-734. doi:10.1080/00029890.1995.12004649DOI: 10.1080/00029890.1995.12004649
THE COLORED JONES FUNCTION (Journal article)
MELVIN, P. M., & MORTON, H. R. (1995). THE COLORED JONES FUNCTION. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 169(3), 501-520. doi:10.1007/BF02099310DOI: 10.1007/BF02099310
MORTON, H. R. (1995). THE COLORED JONES FUNCTION AND ALEXANDER POLYNOMIAL FOR TORUS KNOTS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 117, 129-135. doi:10.1017/S0305004100072959DOI: 10.1017/S0305004100072959
1994
ELRIFAI, E. A., & MORTON, H. R. (1994). ALGORITHMS FOR POSITIVE BRAIDS. QUARTERLY JOURNAL OF MATHEMATICS, 45(180), 479-497. doi:10.1093/qmath/45.4.479DOI: 10.1093/qmath/45.4.479
1993
MORTON, H. R. (1993). QUANTUM INVARIANTS GIVEN BY EVALUATION OF KNOT POLYNOMIALS. Journal of Knot Theory and Its Ramifications, 02(02), 195-209. doi:10.1142/s021821659300012xDOI: 10.1142/s021821659300012x
Morton, H. R. (1993). Invariants of Links and 3-Manifolds From Skein Theory and From Quantum Groups. In Topics in Knot Theory (pp. 107-155). Springer Netherlands. doi:10.1007/978-94-011-1695-4_8DOI: 10.1007/978-94-011-1695-4_8
1992
CROMWELL, P. R., & MORTON, H. R. (1992). POSITIVITY OF KNOT POLYNOMIALS ON POSITIVE LINKS. Journal of Knot Theory and Its Ramifications, 01(02), 203-206. doi:10.1142/s0218216592000112DOI: 10.1142/s0218216592000112
Morton, H. R., & Strickland, P. M. (1992). Satellites and surgery invariants. In A. Kawauchi (Ed.), Knots '90 (pp. 47-66). Amsterdam: Walter de Gruyter.
1991
FIBERED LINKS FROM CLOSED BRAIDS (Journal article)
MONTESINOSAMILIBIA, J. M., & MORTON, H. R. (1991). FIBERED LINKS FROM CLOSED BRAIDS. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 62, 167-201. Retrieved from https://www.webofscience.com/
Fibred Links from Closed Braids (Journal article)
Montesinos-Amilibia, J. M., & Morton, H. R. (1991). Fibred Links from Closed Braids. Proceedings of the London Mathematical Society, s3-62(1), 167-201. doi:10.1112/plms/s3-62.1.167DOI: 10.1112/plms/s3-62.1.167
Montesinos Amilibia, J. M., & Morton, H. R. (1991). Generating fibered Links from closed braids. Proceedings of the London Mathematical Society, 62, 167-201.
MORTON, H. R., & STRICKLAND, P. (1991). JONES POLYNOMIAL INVARIANTS FOR KNOTS AND SATELLITES. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 109, 83-103. doi:10.1017/S0305004100069589DOI: 10.1017/S0305004100069589
Morton, H. R. (1991). Trefoil Knots without Tritangent Planes. Bulletin of the London Mathematical Society, 23(1), 78-80. doi:10.1112/blms/23.1.78DOI: 10.1112/blms/23.1.78
1990
MORTON, H. R., & SHORT, H. B. (1990). CALCULATING THE 2-VARIABLE POLYNOMIAL FOR KNOTS PRESENTED AS CLOSED BRAIDS. JOURNAL OF ALGORITHMS, 11(1), 117-131. doi:10.1016/0196-6774(90)90033-BDOI: 10.1016/0196-6774(90)90033-B
Morton, H., & Traczyk, P. (1990). Knots and algebras. In E. Martin-Peinador, & A. Rodez Usan (Eds.), Contribuciones matematicas en homenaje al profesor D. Antonio Plans Sanz de Bremond (pp. 201-219). Zaragoza: University of Zaragoza.
Morton, H., & Lozano, M. (1990). Pairs of closed 3-braids with the same Alexander polynomial. In E. Martin-Peinador, & U. A. Rodez (Eds.), Contribuciones matematicas en homenaje al profesor D. Antonio Plans Sanz de Bremond (pp. 173-181). Zaragoza: University of Zaragoza.
1989
Threading knot diagrams (by Hugh R. Morton), [Math. Proc. Camb. Phil. Soc. 99(1986), 247–260] (Chapter)
Morton, H. R. (1989). Threading knot diagrams (by Hugh R. Morton), [Math. Proc. Camb. Phil. Soc. 99(1986), 247–260]. In Unknown Book (pp. 171-184). Cambridge University Press. doi:10.1017/cbo9780511613098.007DOI: 10.1017/cbo9780511613098.007
1988
Morton, H. R. (1988). Polynomials from braids. In J. S. Birman, & A. Libgober (Eds.), Braids (Vol. 78, pp. 575-585). Providence, Rhode Island: American Mathematical Society.
Morton, H., & Traczyk, P. (1988). The Jones polynomials of satellites about mutant knots. In J. S. Birman, & A. Libgober (Eds.), Braids (Vol. 78, pp. 587-592). Providence, Rhode Island: American Mathematical Society.
1987
MORTON, H. R., & SHORT, H. B. (1987). THE 2-VARIABLE POLYNOMIAL OF CABLE KNOTS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 101, 267-278. doi:10.1017/S0305004100066627DOI: 10.1017/S0305004100066627
1986
THE JONES POLYNOMIAL FOR UNORIENTED LINKS (Journal article)
MORTON, H. R. (1986). THE JONES POLYNOMIAL FOR UNORIENTED LINKS. QUARTERLY JOURNAL OF MATHEMATICS, 37(145), 55-60. doi:10.1093/qmath/37.1.55DOI: 10.1093/qmath/37.1.55
FIBERED KNOTS OF GENUS-2 FORMED BY PLUMBING HOPF BANDS (Journal article)
MELVIN, P. M., & MORTON, H. R. (1986). FIBERED KNOTS OF GENUS-2 FORMED BY PLUMBING HOPF BANDS. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 34, 159-168. Retrieved from https://www.webofscience.com/
Fibred Knots of Genus 2 Formed by Plumbing Hopf Bands (Journal article)
Melvin, P. M., & Morton, H. R. (1986). Fibred Knots of Genus 2 Formed by Plumbing Hopf Bands. Journal of the London Mathematical Society, s2-34(1), 159-168. doi:10.1112/jlms/s2-34.1.159DOI: 10.1112/jlms/s2-34.1.159
LONG, D. D., & MORTON, H. R. (1986). HYPERBOLIC 3-MANIFOLDS AND SURFACE AUTOMORPHISMS. TOPOLOGY, 25(4), 575-583. doi:10.1016/0040-9383(86)90033-9DOI: 10.1016/0040-9383(86)90033-9
SEIFERT CIRCLES AND KNOT POLYNOMIALS (Journal article)
MORTON, H. R. (1986). SEIFERT CIRCLES AND KNOT POLYNOMIALS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 99, 107-109. doi:10.1017/S0305004100063982DOI: 10.1017/S0305004100063982
THREADING KNOT DIAGRAMS (Journal article)
MORTON, H. R. (1986). THREADING KNOT DIAGRAMS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 99, 247-260. doi:10.1017/S0305004100064161DOI: 10.1017/S0305004100064161
1985
Advice on Hanging Pictures (Journal article)
Bloore, F. J., & Morton, H. R. (1985). Advice on Hanging Pictures. The American Mathematical Monthly, 92(5), 309-321. doi:10.1080/00029890.1985.11971609DOI: 10.1080/00029890.1985.11971609
Morton, H. R. (1985). Exchangeable braids. In R. A. Fenn (Ed.), Low dimensional topology (Vol. 95, pp. 86-105). London: London Mathematical Society.
1984
MORTON, H. R. (1984). ALEXANDER POLYNOMIALS OF CLOSED 3-BRAIDS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 96(SEP), 295-299. doi:10.1017/S0305004100062186DOI: 10.1017/S0305004100062186
1983
AN IRREDUCIBLE 4-STRING BRAID WITH UNKNOTTED CLOSURE (Journal article)
MORTON, H. R. (1983). AN IRREDUCIBLE 4-STRING BRAID WITH UNKNOTTED CLOSURE. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 93(MAR), 259-261. doi:10.1017/S0305004100060540DOI: 10.1017/S0305004100060540
Fibred knots with a given Alexander polynomial (Chapter)
Morton, H. R. (1983). Fibred knots with a given Alexander polynomial. In C. Weber (Ed.), Noeuds, tresses et singularites (Vol. 31, pp. 205-222). Geneva: Universite de Geneve.
1982
CLOSED CURVES WITH NO QUADRISECANTS (Journal article)
MORTON, H. R., & MOND, D. M. Q. (1982). CLOSED CURVES WITH NO QUADRISECANTS. TOPOLOGY, 21(3), 235-243. doi:10.1016/0040-9383(82)90007-6DOI: 10.1016/0040-9383(82)90007-6
1979
A criterion for an embedded surface in R3 to be unknotted (Chapter)
Morton, H. R. (1979). A criterion for an embedded surface in R3 to be unknotted. In R. A. Fenn (Ed.), Topology of low-dimensional manifolds (Vol. 722, pp. 93-98). Heidelberg: Springer.
CLOSED BRAIDS WHICH ARE NOT PRIME KNOTS (Journal article)
MORTON, H. R. (1979). CLOSED BRAIDS WHICH ARE NOT PRIME KNOTS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 86(NOV), 421-426. doi:10.1017/S0305004100056267DOI: 10.1017/S0305004100056267
1978
INFINITELY MANY FIBERED KNOTS HAVING SAME ALEXANDER POLYNOMIAL (Journal article)
MORTON, H. R. (1978). INFINITELY MANY FIBERED KNOTS HAVING SAME ALEXANDER POLYNOMIAL. TOPOLOGY, 17(1), 101-104. doi:10.1016/0040-9383(78)90016-2DOI: 10.1016/0040-9383(78)90016-2
1977
SOME UNEXPECTEDLY NON-SINGULAR ORBIT SPACES (Journal article)
MORTON, H. R. (1977). SOME UNEXPECTEDLY NON-SINGULAR ORBIT SPACES. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 82(JUL), 35-37. doi:10.1017/S0305004100053652DOI: 10.1017/S0305004100053652
1970
Finite orthogonal symmetry (Journal article)
Robertson, S. A., Carter, S., & Morton, H. R. (1970). Finite orthogonal symmetry. Topology, 9(1), 79-95. doi:10.1016/0040-9383(70)90052-2DOI: 10.1016/0040-9383(70)90052-2
Joins of polyhedra (Journal article)
Morton, H. R. (1970). Joins of polyhedra. Topology, 9(3), 243-249. doi:10.1016/0040-9383(70)90014-5DOI: 10.1016/0040-9383(70)90014-5
1967
Symmetric products of the circle (Journal article)
Morton, H. R. (1967). Symmetric products of the circle. Mathematical Proceedings of the Cambridge Philosophical Society, 63(2), 349-352. doi:10.1017/s0305004100041256DOI: 10.1017/s0305004100041256
Space Of Homeomorphisms Of A Disc With N Holes (Journal article)
Morton, H. R. (1967). Space Of Homeomorphisms Of A Disc With N Holes. Illinois Journal Of Mathematics, 11(1), 40.