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Mutation and volumes of knots inS 3

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References

  1. Adams, C.: Thrice-punctured spheres in hyperbolic 3-manifolds. Trans. Am. Math. Soc.287, 645–656 (1985)

    Google Scholar 

  2. Anderson, M.: Complete minimal hypersurfaces in hyperbolicn-manifolds. Comment. Math. Helv.58, 264–290 (1983)

    Google Scholar 

  3. Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of the second order. J. Math. Pures Appl. IX. Ser.36, 235–249 (1957)

    Google Scholar 

  4. Bers, L.: Quasi-conformal mappings and Teichmüller's theorem. In:Analytic function theory, pp. 89–119. Princeton: Princeton University Press (1960)

    Google Scholar 

  5. Bonahon, F.: Bouts des variétés hyperboliques de dimension 3. Ann. Math.124, 71–158 (1986)

    Google Scholar 

  6. Bonahon, F., Siebenmann, L.:Geometric splittings of classical knots, and the algebraic knots of conway. Lond. Math. Soc. Lecture Notes, Cambridge University Press, Cambridge 1987

    Google Scholar 

  7. Conway, J.: An enumeration of knots and links and some of their algebraic properties. In:Computational problems in abstract algebra. New York: Pergamon Press 1970

    Google Scholar 

  8. Cooper, D.: Thesis, Warwick University 1982

  9. Culler, M.: Lifting representations to covering groups. Adv. Math.59, 64–70 (1986)

    Google Scholar 

  10. Culler, M., Shalen, P.: Varieties of group representation and splittings of 3-manifolds. Ann. Math.117, 109–146 (1983)

    Google Scholar 

  11. Freedman, M., Hass, J., Scott, P.: Least area incompressible surfaces in 3-manifolds. Invent. Math.71, 609–642 (1983)

    Google Scholar 

  12. Freyd, P., Yetter, D., Hoste, J., Lickorish, W.B.R., Millett, K., Ocneanu, A.: A new polynomial invariant of knots and links. Bull. Am. Math. Soc.12, 239–246 (1985)

    Google Scholar 

  13. Gromov, M.: Volume and bounded cohomology. Publ. Math., Inst. Hautes Etud. Sci.56, 5–100 (1982)

    Google Scholar 

  14. Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math.97, 275–305 (1973)

    Google Scholar 

  15. Hass, J., Scott, P.: The existence of least area surfaces. MSRI Preprint, 1985

  16. Jaco, W., Rubinstein, H.: Lectures onPL minimal surfaces. MSRI (1985)

  17. Jaco, W., Shalen, P.: Seifert fibered spaces in 3-manifolds. Mem. Am. Math. Soc.220, (1979)

  18. Johannson, K.: Homotopy equivalences of 3-manifolds with boundary. Lecture Notes in Math., vol. 761. Berlin-Heidelberg-New York: 1979

  19. Kra, I.: On lifting Kleinian groups to SL2(C). In:Differential geometry and complex analysis, pp. 181–194, Chavel, I., Farkas, H. (eds.). Berlin-Heidelberg-New York-Tokyo: Springer 1985

    Google Scholar 

  20. Meeks, W., Scott, P.: Finite group actions on 3-manifolds. Invent. Math.86, 287–346 (1986)

    Google Scholar 

  21. Meeks, W., Scott, P., Yau, S.T.: The classical Plateau problem and the topology of three-dimensional manifolds. Topology21, 409–440 (1982)

    Google Scholar 

  22. Montesinos, J.M.: Revêtements ramifies de noeuds, espaces de Seifert et scindements de Heegard. Orsay preprint 1980

  23. Morrey, C.B.: The problem of Plateau in a Riemannian manifold. Ann. Math.49, 807–851 (1948)

    Google Scholar 

  24. Neumann, W., Zagier, D.: Volumes of hyperbolic manifolds. Preprint 1983

  25. Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math.113, 1–24 (1981)

    Google Scholar 

  26. Schoen, R., Yau, S.T.: Existence of incompressible minimal surfaces and the topology of 3-dimensional manifolds with non-negative scalar curvature. Ann. Math.110, 127–142 (1979)

    Google Scholar 

  27. Scott, P.: Subgroups of surface groups are almost geometric. J. Lond. Math. Soc., II. Ser.17, 555–565 (1978)

    Google Scholar 

  28. Selberg, A.: On discontinuous groups acting in higher dimensional symmetric space. In:Contributions to function theory, pp. 147–164. Tata Institute, Bombay 1960

    Google Scholar 

  29. Siebenmann, L.: On the vanishing of the Rochlin invariant and non-finitely amphicheiral homology 3-spheres. In: Lect. Notes Math. vol. 788, pp. 223–244. Berlin-Heidelberg-New York: 1980

  30. Thurston, W.: Geometry and topology of 3-manifolds. Princeton: Princeton University Press 1978

    Google Scholar 

  31. Waldhausen, F.: On irreducible 3-manifolds which are sufficiently large. Ann. Math.87, 56–88 (1968)

    Google Scholar 

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Ruberman, D. Mutation and volumes of knots inS 3 . Invent Math 90, 189–215 (1987). https://doi.org/10.1007/BF01389038

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