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On central extensions of mapping class groups

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References

  1. M.F. Atiyah. The logarithm of the Dedekind η-function, Math. Ann.278 (1987) 335–380

    Google Scholar 

  2. M.F. Atiyah. Topological quantum field theories, Publ. Math. IHES68 (1989), 175–186

    Google Scholar 

  3. M.F. Atiyah. On framings of 3-manifolds, Topology29 (1990), 1–7

    Google Scholar 

  4. J. Barge, E. Ghys. Cocycles d'Euler et de Maslov, Math. Ann.294 (1992) 235–265

    Google Scholar 

  5. C. Blanchet, N. Habegger, G. Masbaum, P. Vogel. Three-manifold invariants derived from the Kauffman bracket, Topology31 (1992), 685–699

    Google Scholar 

  6. C. Blanchet, N. Habegger, G. Masbaum, P. Vogel. Topological quantum field theories derived from the Kauffman bracket, to appear in Topology (Nantes Preprint May 1992)

  7. R.A. Fenn, C.P. Rourke. Racks and Links in Codimension Two, Journal of Knot Theory and its Ramifications, Vol. 1 No. 4 (1992) 343–406

    Google Scholar 

  8. D.S. Freed, R.E. Gompf. Computer calculations of Witten's 3-manifold invariant, Comm. Math. Phys.141 (1991), 79–117

    Google Scholar 

  9. S. Gervais. Thèse, Nantes, January 1994

  10. S. Gervais. Presentations and extensions of mapping class groups, Nantes Preprint May 1994

  11. J. Harer. Thé second homology group of the mapping class group of an orientable surface, Invent. Math.72 (1983), 221–239

    Google Scholar 

  12. J. Harer. The Cohomology of the Moduli Space of Curves, in: E. Sernesi (Ed.), Theory of Moduli, Springer LNM 1337

  13. A. Hatcher, W. Thurston. A presentation of the mapping class group of a closed orientable surface, Topology19 (1980), 221–237

    Google Scholar 

  14. L.H. Kauffman. State models and the Jones polynomial, Topology26 (1987), 395–401

    Google Scholar 

  15. R.C. Kirby, P. Melvin. Dedekind sums, mu invariants and the signature cocycle Math. Ann.299, 231–267 (1994)

    Google Scholar 

  16. T. Kohno. Topological invariants for 3-manifolds using representations of mapping class groups I, Topology31 (1992), 203

    Google Scholar 

  17. W.B.R. Lickorish. Three-manifolds and the Temperley-Lieb algebra, Math. Ann.290 (1990), 657–670

    Google Scholar 

  18. W.B.R. Lickorish. Calculations with the Temperley-Lieb algebra, Comm. Math. Helv.67 (1992), 571–591

    Google Scholar 

  19. W.B.R. Lickorish. Skeins and handlebodies, Pac. J. Math. 159 No. 2 (1993) 337–350

    Google Scholar 

  20. N. Lu. Homeomorphisms of a handlebody and Heegaard splittings of the 3-sphereS 3, Top. Proc.13 (1988) 325–350

    Google Scholar 

  21. N. Lu. A simple proof of the fundamental theorem of Kirby calculus on links, Trans. AMS, vol 331 No 1 (1992) 143–156

    Google Scholar 

  22. G. Masbaum, P. Vogel. Verlinde formulae for surfaces with spin structure, Proceedings of the Joint US-Israel workshop on geometric topology, Haifa, June 1992. Contemp. Math.164, 119–137 (1994)

    Google Scholar 

  23. W. Meyer. Die Signatur von Flächenbündeln, Math. Ann.201 (1973), 239–264

    Google Scholar 

  24. H. Morton. Invariants of links and 3-manifolds from skein theory and from quantum groups, in Topics in Knot Theory, ed. Bozhüyük, Kluwer (to appear)

  25. H. Morton, P. Strickland. Satellites and surgery invariants, in “Knots 90” ed. A. Kawauchi, de Gruyter (1992).

  26. N.Yu. Reshetikhin, V.G. Turaev. Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math.103 (1991), 547–597

    Google Scholar 

  27. J.D. Roberts. Skeins and mapping class groups, Math. Proc. Camb. Phil. Soc.115 (1994) 53–77

    Google Scholar 

  28. J.D. Roberts. Ph.D. Thesis, Cambridge, April 1994

  29. R. Stong. Notes on cobordism theory, Princeton Math. Notes, PUP (1958)

  30. S. Suzuki. On homeomorphisms of a 3-dimensional handlebody, Canad. J. Math.29 (1977) 111–124

    Google Scholar 

  31. V. Turaev, H. Wenzl, Quantum invariants of 3-manifolds associated with classical simple Lie algebras, Int. J. Math. Vol. 4 No. 2 (1993) 323–358

    Google Scholar 

  32. B. Wajnryb. A simple presentation for the mapping class group of an orientable surface, Israel J. Math.45 (1983), 157–174

    Google Scholar 

  33. K. Walker. On Witten's 3-manifold invariants, preprint (1991)

  34. H. Wenzl. Braids and Invariants of 3-manifolds, Inv. Math.114 (1993), 235–275

    Google Scholar 

  35. E. Witten. Quantum field theory and the Jones polynomial, Comm. Math. Phys.121 (1989), 351–399

    Google Scholar 

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Masbaum, G., Roberts, J.D. On central extensions of mapping class groups. Math. Ann. 302, 131–150 (1995). https://doi.org/10.1007/BF01444490

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  • DOI: https://doi.org/10.1007/BF01444490

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