On the algebraic structure of link-diagrams on a 2-dimensional surface

Paolo Cotta-Ramusino; Maurizio Rinaldi

doi:10.1007/bf02099672

journal article May 01, 1991

On the algebraic structure of link-diagrams on a 2-dimensional surface

Paolo Cotta-Ramusino Maurizio Rinaldi

Communications in Mathematical Physics Vol. 138 No. 1 pp. 137-173 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf02099672

Topics

No keywords indexed for this article. Browse by subject →

References

28

[1]

A polynomial invariant for knots via von Neumann algebras

Vaughan F. R. Jones

Bulletin of the American Mathematical Society 1985 10.1090/s0273-0979-1985-15304-2

[2]

Akutsu, Y., Deguchi, T., Wadati, M.: Exactly solvable models and new Link polynomials I, II, J. Phys. Soc. Jpn.56, 3039–3051 and 3464–3479 (1987) 10.1143/jpsj.56.3039

[3]

Atiyah, M.F.: New invariants of three and four dimensional manifolds in the mathematical Heritage of Hermann Weyl, Proc. Symp. Pure Math.48, Wells, R. (ed.) pp. 285–299 (1988) 10.1090/pspum/048/974342

[4]

Witten, E.: Quantum field theory and the Jones Polynomial, Commun. Math. Phys.121, 351–399 (1989) 10.1007/bf01217730

[5]

Alvarez-Gaumé, L., Gomez, G., Sierra, G.: Topics in conformal field theory, CERN preprint TH 5540/89

[6]

Drinfel'd, V.G.: Quantum groups. Proceedings of the International Congress of Mathematicians, Berkeley, CA., USA, 798–820 (1986)

[7]

Freyd, P., Yetter, D., Hoste, J., Lickorish, W.B.R., Millet, K.C., Ocneanu, A.: A new polynomial invariant of Knots and Links. Bull AMS12, 239–246 (1985) 10.1090/s0273-0979-1985-15361-3

[8]

Turaev, V.G.: The Yang-Baxter equation and Invariants of Links. Inv. Math.92, 527–553 (1988) 10.1007/bf01393746

[9]

Reshetikhin, N.Yu.: Quantized universal Enveloping Algebras and Invariants of Links, I, II, LOMI preprints E-4-87 and E-17-87 (1987)

[10]

Turaev, V.G.: Skein quantization of Poisson algebras of Loops on surfaces, LOMI preprint (July 1989)

[11]

Turaev, V.G.: Algebras of loops on surfaces, algebras of Knots and quantization. In: Braid group, Knot theory and Statistical Mechanics, Yang, C.N., Ge, M.L. (eds.). Singapore: World Scientific 1989

[12]

Goldman, W. M.: Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Inv. Math.86, 263–302 (1986) 10.1007/bf01389091

[13]

Cotta-Ramusino, P., Rinaldi, M.: Link-diagrams, Yang-Baxter equations and Quantum Holonomy, Harvard preprint (Feb. 1991) 10.1090/conm/134/1187277

[14]

Cotta-Ramusiono, P., Rinaldi, M., Stasheff, J.: In preparation

[15]

Ramadas, T.R., Singer, I.M., Weitsman, J.: Some comments on Chern-Simons Gauge Theorey. Commun. Math. Phys.126, 409–420 (1989) 10.1007/bf02125132

[16]

Segal, G.: The Abelian theory in Oxford seminar on Jones-Witten theory. Oxford University, Michaelmas Term (1989)

[17]

Jaeger, F.: Composition products and models for the Homfly polynomial. Preprint, Grenoble (1988)

[18]

Jones, V.F.R.: On knot invariants related to some statistical mechanics models. Pac. J. Math.137, 311–334 (1989) 10.2140/pjm.1989.137.311

[19]

State models and the jones polynomial

Louis H. Kauffman

Topology 1987 10.1016/0040-9383(87)90009-7

[20]

Drinfel'd, V.G.: Quasi Hopf Algebras and Knizhnik-Zamolodchikov Equations, preprint, Institute of Theoretical Physics, USSR Academy (1989) 10.1007/978-3-642-84000-5_1

[21]

Baxter, R.: Exactly solved models in statistical mechanics. New York, London: Academic Press 1982

[22]

Kauffman, L.: On Knots. Princeton, N.J.: Princeton University Press 1987

[23]

Reinhart, B.L.: The Winding Number on two Manifolds. Ann. Inst. Fourier, Grenoble10, 271–283 (1960) 10.5802/aif.100

[24]

Reinhart, B.L.: Further remarks on the winding number. Ann. Inst. Fourier, Grenoble13, 155–160 (1963) 10.5802/aif.136

[25]

Chillingworth, D.R.J.: Winding numbers on surfaces, I. Math. Ann.196, 218–249 (1972) 10.1007/bf01428050

[26]

Chillingworth, D.R.J.: Winding numbers on surfaces, II. Math. Ann.199, 131–153 (1972) 10.1007/bf01431419

[27]

Milnor, J.W., Moore, J.C.: On the structure of Hopf Algebras. Ann. Math. (2)81, 211–264 (1965) 10.2307/1970615

[28]

De La Harpe, P., Kervaire, M., Weber, C.: On the Jones Polynomials. L'Ens. Math.32, 271–335 (1986)

Cited By

9

A Lower Bound for the Crossing Number of Links in Thickened Surfaces

V. V. Tarkaev · 2018

Siberian Mathematical Journal

Metrics

9

Citations

28

References

Details

Published: May 01, 1991
Vol/Issue: 138(1)
Pages: 137-173
License: View

Authors

Cite This Article

Paolo Cotta-Ramusino, Maurizio Rinaldi (1991). On the algebraic structure of link-diagrams on a 2-dimensional surface. Communications in Mathematical Physics, 138(1), 137-173. https://doi.org/10.1007/bf02099672

On the algebraic structure of link-diagrams on a 2-dimensional surface

You May Also Like