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Properties of Viro--Turaev Representations of the Mapping Class Group of a Torus

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Matrix realizations for the Turaev―Viro representations of the mapping class group of a torus are constructed. Each of the representations is generated by three involutive matrices. The finiteness of the representations is proved for the levels \(r = 3,4,5,6\). Bibliography: 13 titles.

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REFERENCES

  1. M. Atiyah, The Geometry and Physics of Knots, Cambridge Univ. Press, Cambridge-New York-Port Chester-Melbourne-Sydney (1990).

    Google Scholar 

  2. G. Wright, “The Reshetikhin-Turaev representation of the mapping class group,” J. Knot Theory Ramifications, 3, 547–574(1994).

    Google Scholar 

  3. G. Wright, “The Reshetikhin-Turaev representation of the mapping class groups at sixth root of unity,” J. Knot Theory Ramifications, 5, 721–741(1996).

    Google Scholar 

  4. T. Kohno, “Topological invariants of 3-manifolds using representations of mapping class group,” Topology, 31, 203–230(1992).

    Google Scholar 

  5. L. C. Jeffrey, “Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation,” Commun. Math. Phys., 147, 563–604(1992).

    Google Scholar 

  6. V. G. Turaev and O. Ya. Viro, “State sum invariants of 3-manifolds and quantum 6j-symbols,” Topology, 31, 865–902(1992).

    Google Scholar 

  7. V. G. Turaev, Quantum Invariants of Knots and 3-Manifolds, (de Gruyter Studies Math., 18), de Gruyter (1994).

  8. J. Roberts, “Skein-theory and the Turaev-Viro invariants,” preprint (1993).

  9. M. A. Ovchinnikov, “Presentation of homeotopies of the torus by simple polyhedra with boundary,” Mat. Zametki, 66, 593–540(1999).

    Google Scholar 

  10. B. G. Casler, “An embedding theorem for connected 3-manifolds with boundary,” Proc. Amer. Math. Soc., 16, 559–566(1965).

    Google Scholar 

  11. S. V. Matveev, “Special skeleta of piecewise linear manifolds,” Mat. Sb., 92(134), No. 2, 282–293(1973).

    Google Scholar 

  12. S. V. Matveev, “Transformations of special spines and the Zeeman conjecture,” Izv. Akad. Nauk SSSR, 51, 1104–1115(1987).

    Google Scholar 

  13. M. V. Sokolov, “The Turaev-Viro invariant for 3-manifold is a sum of three invariants,” Canad. Math. Bull., 39, 468–475(1996).

    Google Scholar 

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Ovchinnikov, M.A. Properties of Viro--Turaev Representations of the Mapping Class Group of a Torus. Journal of Mathematical Sciences 113, 856–867 (2003). https://doi.org/10.1023/A:1021299705329

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