Publications
Selected publications
- The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra (Journal article - 2014)
- Mutant knots with symmetry (Journal article - 2007)
- Geometrical relations and plethysms in the Homfly skein of the annulus (Journal article - 2007)
- Mutant Knots (Chapter - 2015)
- Relations between Kauffman and Homfly satellite invariants (Journal article - 2009)
2024
The braid indices of the reverse parallel links of alternating knots
Diao, Y., & Morton, H. (2024). The braid indices of the reverse parallel links of alternating knots. Algebraic & Geometric Topology, 24(5), 2957-2970. doi:10.2140/agt.2024.24.2957
2023
Tangles in affine Hecke algebras
Morton, H. (2023). Tangles in affine Hecke algebras. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. doi:10.1142/S0218216523400187
The Braid Indices of the Reverse Parallel Links of Alternating Knots
Diao, Y., & Morton, H. (2023). The Braid Indices of the Reverse Parallel Links of Alternating Knots. Algebr. Geom. Topol., 24, 2957-2970. Retrieved from http://dx.doi.org/10.2140/agt.2024.24.2957
The Braid Indices of the Reverse Parallel Links of Alternating Knots
2022
2021
DAHAs and skein theory
Morton, H., & Samuelson, P. (2021). DAHAs and skein theory. Communications in Mathematical Physics. Retrieved from http://arxiv.org/abs/1909.11247v2
2020
Satellites and quantum invariants
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
Mutant Knots
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
The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra
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:10.1215/00127094-3718881
The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra
2011
KNOTS, SATELLITES AND QUANTUM GROUPS
Morton, H. R. (2011). KNOTS, SATELLITES AND QUANTUM GROUPS. In Series on Knots and Everything (pp. 379-406). WORLD SCIENTIFIC. doi:10.1142/9789814313001_0014
2010
A basis for the Birman-Wenzl algebra
Morton, H. R. (2010). A basis for the Birman-Wenzl algebra. Retrieved from http://arxiv.org/abs/1012.3116v1
THE SL<sub>3</sub> COLORED JONES POLYNOMIAL OF THE TREFOIL
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/S0002-9939-2013-11582-0
The SL_3 colored Jones polynomial of the trefoil
2009
Relations between Kauffman and Homfly satellite invariants
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/S0305004110000058
Relations between Kauffman and Homfly satellite invariants
2008
DOUBLY PERIODIC TEXTILE STRUCTURES
Morton, H. R., & Grishanov, S. (2009). DOUBLY PERIODIC TEXTILE STRUCTURES. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 18(12), 1597-1622. doi:10.1142/S0218216509007646
Doubly periodic textile patterns
2007
INVARIANTS OF GENUS 2 MUTANTS
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/S0218216509007506
Invariants of genus 2 mutants
Geometrical relations and plethysms in the Homfly skein of the annulus
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/jdn026
Geometrical relations and plethysms in the Homfly skein of the annulus
Mutant knots with symmetry
Morton, H. R. (2009). Mutant knots with symmetry. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 146, 95-107. doi:10.1017/S0305004108001862
Mutant knots with symmetry
2006
The Alexander polynomial of a torus knot with twists
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/S0218216506004920
Integrality of Homfly (1,1)-tangle invariants
Integrality of Homfly 1-tangle invariants
Morton, H. R. (2007). Integrality of Homfly 1-tangle invariants. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 7, 327-338. doi:10.2140/agt.2007.7.327
Murphy operators in Knot Theory
Morton, H. R. (2006). Murphy operators in Knot Theory. In Unknown Book (Vol. 10, pp. 359-366). doi:10.1142/9789812772527_0031
2004
A basis for the full Homfly skein of the annulus
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/S0305004105009047
A basis for the full Homfly skein of the annulus
2003
Conjugacy for positive permutation braids
Morton, H. R., & Hadji, R. J. (2005). Conjugacy for positive permutation braids. FUNDAMENTA MATHEMATICAE, 188, 155-166. doi:10.4064/fm188-0-8
Conjugacy for positive permutation braids
2001
Power sums and Homfly skein theory
Morton, H. R. (2001). Power sums and Homfly skein theory. Geom. Topol. Monogr., 4, 235-244. Retrieved from http://arxiv.org/abs/math/0111101v3
The Homfly polynomial of the decorated Hopf link
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/S0218216503002536
The Homfly polynomial of the decorated Hopf link
Homfly Polynomials of Generalized Hopf Links
Homfly polynomials of generalized Hopf links
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.2002.2.11
Skein theory and the Murphy operators
Morton, H. R. (2002). Skein theory and the Murphy operators. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 11(4), 475-492. doi:10.1142/S0218216502001767
2000
The spread and extreme terms of Jones polynomials
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/S0218216503002512
MUTUAL BRAIDING AND THE BAND PRESENTATION OF BRAID GROUPS
MORTON, H. R., & RAMPICHINI, M. (2000). MUTUAL BRAIDING AND THE BAND PRESENTATION OF BRAID GROUPS. In Knots in Hellas '98 (pp. 335-346). WORLD SCIENTIFIC. doi:10.1142/9789812792679_0020
1999
Mutual braiding and the band presentation of braid groups
Morton, H. R., & Rampichini, M. (1999). Mutual braiding and the band presentation of braid groups. Retrieved from http://arxiv.org/abs/math/9907017v1
Mutual braiding and the band presentation of braid groups
Multiburau
Morton, H., & Hodgson, J. (1999). Multiburau [Computer Software].
1998
Mutants and SU(3)_q invariants
Morton, H. R., & Ryder, H. J. (1998). Mutants and SU(3)_q invariants. Retrieved from http://arxiv.org/abs/math/9810197v1
The Multivariable Alexander Polynomial for a Closed Braid
Morton, H. R. (1998). The Multivariable Alexander Polynomial for a Closed Braid. Retrieved from http://arxiv.org/abs/math/9803138v1
The Burau matrix and Fiedler's invariant for a closed braid
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)00009-1
Arc index and the Kauffman polynomial
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/s0305004197002090
1997
Idempotents of Hecke algebras of type A
Idempotents of Hecke algebras of type A.
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/S0218216598000243
Young diagrams, the Homfly skein of the annulus and unitary invariants
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
Distinguishing mutants by knot polynomials
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/S0218216596000163
Unitary quantum groups and mutant knots
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
Fibonacci-like Sequences and Greatest Common Divisors
Morton, H. R. (1995). Fibonacci-like Sequences and Greatest Common Divisors. The American Mathematical Monthly, 102(8), 731-734. doi:10.1080/00029890.1995.12004649
THE COLORED JONES FUNCTION
MELVIN, P. M., & MORTON, H. R. (1995). THE COLORED JONES FUNCTION. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 169(3), 501-520. doi:10.1007/BF02099310
THE COLORED JONES FUNCTION AND ALEXANDER POLYNOMIAL FOR TORUS KNOTS
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/S0305004100072959
1994
ALGORITHMS FOR POSITIVE BRAIDS
ELRIFAI, E. A., & MORTON, H. R. (1994). ALGORITHMS FOR POSITIVE BRAIDS. QUARTERLY JOURNAL OF MATHEMATICS, 45(180), 479-497. doi:10.1093/qmath/45.4.479
1993
QUANTUM INVARIANTS GIVEN BY EVALUATION OF KNOT POLYNOMIALS
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/s021821659300012x
Invariants of Links and 3-Manifolds From Skein Theory and From Quantum Groups
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_8
1992
POSITIVITY OF KNOT POLYNOMIALS ON POSITIVE LINKS
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/s0218216592000112
Satellites and surgery invariants
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
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
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/s3-62.1.167
Generating fibered Links from closed braids
Montesinos Amilibia, J. M., & Morton, H. R. (1991). Generating fibered Links from closed braids. Proceedings of the London Mathematical Society, 62, 167-201.
JONES POLYNOMIAL INVARIANTS FOR KNOTS AND SATELLITES
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/S0305004100069589
Trefoil Knots without Tritangent Planes
Morton, H. R. (1991). Trefoil Knots without Tritangent Planes. Bulletin of the London Mathematical Society, 23(1), 78-80. doi:10.1112/blms/23.1.78
1990
CALCULATING THE 2-VARIABLE POLYNOMIAL FOR KNOTS PRESENTED AS CLOSED BRAIDS
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-B
Knots and algebras
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.
Pairs of closed 3-braids with the same Alexander polynomial
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]
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/cbo9780511613098.007
1988
Polynomials from braids
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.
The Jones polynomials of satellites about mutant knots
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
THE 2-VARIABLE POLYNOMIAL OF CABLE KNOTS
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/S0305004100066627
1986
THE JONES POLYNOMIAL FOR UNORIENTED LINKS
MORTON, H. R. (1986). THE JONES POLYNOMIAL FOR UNORIENTED LINKS. QUARTERLY JOURNAL OF MATHEMATICS, 37(145), 55-60. doi:10.1093/qmath/37.1.55
FIBERED KNOTS OF GENUS-2 FORMED BY PLUMBING HOPF BANDS
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
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/s2-34.1.159
HYPERBOLIC 3-MANIFOLDS AND SURFACE AUTOMORPHISMS
LONG, D. D., & MORTON, H. R. (1986). HYPERBOLIC 3-MANIFOLDS AND SURFACE AUTOMORPHISMS. TOPOLOGY, 25(4), 575-583. doi:10.1016/0040-9383(86)90033-9
SEIFERT CIRCLES AND KNOT POLYNOMIALS
MORTON, H. R. (1986). SEIFERT CIRCLES AND KNOT POLYNOMIALS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 99, 107-109. doi:10.1017/S0305004100063982
THREADING KNOT DIAGRAMS
MORTON, H. R. (1986). THREADING KNOT DIAGRAMS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 99, 247-260. doi:10.1017/S0305004100064161
1985
Advice on Hanging Pictures
Bloore, F. J., & Morton, H. R. (1985). Advice on Hanging Pictures. The American Mathematical Monthly, 92(5), 309-321. doi:10.1080/00029890.1985.11971609
Advice on Hanging Pictures
Bloore, F. J., & Morton, H. R. (1985). Advice on Hanging Pictures. The American Mathematical Monthly, 92(5), 309. doi:10.2307/2323121
Exchangeable braids
Morton, H. R. (1985). Exchangeable braids. In R. A. Fenn (Ed.), Low dimensional topology (Vol. 95, pp. 86-105). London: London Mathematical Society.
1984
ALEXANDER POLYNOMIALS OF CLOSED 3-BRAIDS
MORTON, H. R. (1984). ALEXANDER POLYNOMIALS OF CLOSED 3-BRAIDS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 96(SEP), 295-299. doi:10.1017/S0305004100062186
1983
AN IRREDUCIBLE 4-STRING BRAID WITH UNKNOTTED CLOSURE
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/S0305004100060540
Fibred knots with a given Alexander polynomial
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
MORTON, H. R., & MOND, D. M. Q. (1982). CLOSED CURVES WITH NO QUADRISECANTS. TOPOLOGY, 21(3), 235-243. doi:10.1016/0040-9383(82)90007-6
1979
A criterion for an embedded surface in R3 to be unknotted
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
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/S0305004100056267
1978
INFINITELY MANY FIBERED KNOTS HAVING SAME ALEXANDER POLYNOMIAL
MORTON, H. R. (1978). INFINITELY MANY FIBERED KNOTS HAVING SAME ALEXANDER POLYNOMIAL. TOPOLOGY, 17(1), 101-104. doi:10.1016/0040-9383(78)90016-2
1977
SOME UNEXPECTEDLY NON-SINGULAR ORBIT SPACES
MORTON, H. R. (1977). SOME UNEXPECTEDLY NON-SINGULAR ORBIT SPACES. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 82(JUL), 35-37. doi:10.1017/S0305004100053652
1970
Finite orthogonal symmetry
Robertson, S. A., Carter, S., & Morton, H. R. (1970). Finite orthogonal symmetry. Topology, 9(1), 79-95. doi:10.1016/0040-9383(70)90052-2
Joins of polyhedra
Morton, H. R. (1970). Joins of polyhedra. Topology, 9(3), 243-249. doi:10.1016/0040-9383(70)90014-5
1967
The space of homeomorphisms of a disc with $n$ holes
Morton, H. R. (1967). The space of homeomorphisms of a disc with $n$ holes. Illinois Journal of Mathematics, 11(1). doi:10.1215/ijm/1256054781
Symmetric products of the circle
Morton, H. R. (1967). Symmetric products of the circle. Mathematical Proceedings of the Cambridge Philosophical Society, 63(2), 349-352. doi:10.1017/s0305004100041256