Skip to main content
SpringerLink
Log in

Topological Invariants for Lens Spaces and Exceptional Quantum Groups

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

The Reshetikhin–Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras G2, F4 and E8 at odd roots of unity are constructed and explicitly computed for all the lens spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kauffman, L.: Knots and Physics, World Scientific, Singapore, 1991.

    Google Scholar 

  2. Turaev, V. G.: Quantum Invariants of Knots and 3-Manifolds, de Gruyter, Berlin, New York, 1994.

    Google Scholar 

  3. Witten, E.: Comm. Math. Phys. 121 (1989), 351.

    Google Scholar 

  4. Reshetikhin, N. Yu and Turaev, V. G.: Invent. Math. 10 (1991), 547.

    Google Scholar 

  5. Kohno, T.: Topology, 31 (1992), 203; Crane, L.: Comm. Math. Phys. 135 (1991), 615.

    Google Scholar 

  6. Axelrod, S. and Singer, I.: Chern-Simons perturbation theory, in: Proc. XXth Conference on Differential Geometrical Methods in Physics, World Scientific, Singapore, 1991, pp. 3-45.

    Google Scholar 

  7. Freed, D. and Gompf, R.: Comm. Math. Phys. 141 (1991), 79.

    Google Scholar 

  8. Jeffry, L.: Comm. Math. Phys. 147 (1992), 563.

    Google Scholar 

  9. Rozansky, L.: A large k asymptotics of Witten's invariants of Seifert manifolds, Texas preprint UTTG-06-93.

  10. Kirby R. C. and Melvin, P.: Invent. Math. 105 (1991), 473.

    Google Scholar 

  11. Murakami, H.: Math. Proc. Cambridge Philos. Soc. 115 (1994), 253.

    Google Scholar 

  12. Turaev, V. and Wenzl, H.: Internat. J. Math. 4 (1993), 323; Lyubashenko, V. V.: Comm. Math. Phys. 172 (1995), 467.

    Google Scholar 

  13. Zhang, R. B. and Carey, A. L.: Comm. Math. Phys. 182 (1996), 619.

    Google Scholar 

  14. Zhang, R. B.: Rev. Math. Phys. 7 (1995), 809.

    Google Scholar 

  15. Drinfeld, V. G.: Quantum groups, Proc. ICM, Berkeley, 1986, pp. 798; Jimbo, M.: Lett. Math. Phys. 10 (1985), 63.

  16. Andersen, H. H. and Paradowski, J.: Comm. Math. Phys. 169 (1995), 563.

    Google Scholar 

  17. Lusztig, G.: Introduction to Quantum Groups, Birkhäuser, Basel, 1994; De Concini, C. and Kac, V. G.: Representations of quantum groups at roots of unity, in: A. Connes et al. (eds), Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory, Prog. Math. 92, Birkhäuser, Basel, 1990, p. 471.

  18. Lickorish, W. B. R.: Annals of Math. 76 (1962), 531.

    Google Scholar 

  19. Kirby, R.: Invent. Math. 45 (1978), 35.

    Google Scholar 

  20. Fenn, R. and Rourke, C.: Topology 18 (1979), 1.

    Google Scholar 

  21. Turaev, V. G. and Viro, O. Y.: Topology 31 (1992), 865; Beliakova, A. and Durhuus, A.: On relation between two quantum group invariants of 3-cobordisms, Preprint, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of Adelaide, Adelaide, Australia. e-mail

    R. B. ZHANG

Authors
  1. R. B. ZHANG
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

ZHANG, R.B. Topological Invariants for Lens Spaces and Exceptional Quantum Groups. Letters in Mathematical Physics 41, 1–11 (1997). https://doi.org/10.1023/A:1007366912839

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007366912839

Search

Navigation