EXAMPLES OF RIGID AND FLEXIBLE SEIFERT FIBRED CONE-MANIFOLDS
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 411-429

Voir la notice de l'article provenant de la source Cambridge University Press

The present paper gives an example of a rigid spherical cone-manifold and that of a flexible one, which are both Seifert fibred.
DOI : 10.1017/S0017089512000651
Mots-clés : 53A35, 57R18, 57M25
KOLPAKOV, ALEXANDER. EXAMPLES OF RIGID AND FLEXIBLE SEIFERT FIBRED CONE-MANIFOLDS. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 411-429. doi: 10.1017/S0017089512000651
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[1] 1.Boileau, M., Leeb, B. and Porti, J., Uniformization of small 3-orbifolds, C.R. Acad. Sci. Paris Se'r. I Math. 332 (1) (2001), 57–62. Google Scholar

[2] 2.Boileau, M., Leeb, B. and Porti, J., Geometrization of 3-dimensional orbifolds, Ann. Math. 162 (1) (2005), 195–250. Google Scholar

[3] 3.Burago, Y., Gromov, M. and Perelman, G., A. D. Aleksandrov spaces with curvature bounded below, Russian Math. Surveys 47 (1992), 1–58. Google Scholar

[4] 4.Burde, G. and Murasugi, K., Links and Seifert fiber spaces, Duke Math. J. 37 (1) (1970), 89–93. Google Scholar

[5] 5.Casson, A., An example of weak non-rigidity for cone manifolds with vertices, Talk at the Third MSJ regional workshop (Tokyo, 1998). Google Scholar

[6] 6.Cooper, D., Hodgson, C. and Kerckhoff, S., Three-dimensional orbifolds and cone-manifolds', vol. 5, Postface by Kojima, S.. Tokyo: Mathematical Society of Japan, 2000. (MSJ Memoirs) Google Scholar

[7] 7.Culler, M., Lifting representations to covering groups, Adv. Math. 59 (1) (1986), 64–70. Google Scholar | DOI

[8] 8.Dunbar, W. D., Geometric orbifolds, Rev. Mat. Univ. Complut. Madrid 1 (1988), 67–99. Google Scholar

[9] 9.Gluck, H. and Ziller, W., The geometry of the Hopf fibrations, L'Enseign. Math. 32 (1986), 173–198. Google Scholar

[10] 10.Goldman, W., Ergodic theory on moduli spaces, Ann. Math. 146 (3) (1997), 475–507. Google Scholar | DOI

[11] 11.Hilden, H. M., Lozano, M. T. and Montesinos-Amilibia, J.-M., Volumes and Chern-Simons invariants of cyclic coverings over rational knots, in Proceedings of the 37th Taniguchi symposium on topology and teichmuller spaces held in Finland, July 1995 (Kojima, S., Matsumoto, Y., Saito, K. and Seppälä, M., Editors) (1996), 31–35. Google Scholar

[12] 12.Hodgson, C., Degeneration and regeneration of hyperbolic structures on three-manifolds, Thesis (Princeton, 1986). Google Scholar

[13] 13.Hodgson, C. and Kerckhoff, S., Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Diff. Geom. 48 (1) (1998), 1–59. Google Scholar

[14] 14.Hopf, H., Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche, Math. Ann. 104 (1931), 637–665. Google Scholar

[15] 15.Izmestiev, I., Examples of infinitesimally flexible 3-dimensional hyperbolic cone-manifolds, J. Math. Soc. Japan 63 (2) (2011), 581–598. Google Scholar

[16] 16.Kojima, S., Deformations of hyperbolic 3-cone-manifolds, J. Diff. Geom. 49 (3) (1998), 469–516. Google Scholar

[17] 17.Kolpakov, A. A. and Mednykh, A. D., Spherical structures on torus knots and links, Siberian Math. J. 50 (5) (2009), 856–866. Google Scholar

[18] 18.Montcouquiol, G., Deformation of hyperbolic convex polyhedra and 3-cone-manifolds, Geom. Dedicata (2012), arXiv:0903.4743. Google Scholar

[19] 19.Mostow, G. D., Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Etudes Sci. Publ. Math. 34 (1968), 53–104. Google Scholar

[20] 20.Porti, J., Regenerating hyperbolic and spherical cone structures from Euclidean ones, Topology 37 (2) (1998), 365–392. Google Scholar

[21] 21.Porti, J., Regenerating hyperbolic cone structures from Nil, Geom. Topol. 6 (2002), 815–852. Google Scholar

[22] 22.Porti, J., Spherical cone structures on 2-bridge knots and links, Kobe J. Math. 21 (1–2) (2004), 61–70. Google Scholar

[23] 23.Porti, J., Regenerating hyperbolic cone 3-manifolds from dimension 2, Ann. Inst. Fourier, arXiv:1003.2494. Google Scholar

[24] 24.Prasad, G., Strong rigidity of -rank 1 lattices, Invent. Math. 21 (1973), 255–286. Google Scholar

[25] 25.Ratcliffe, J., Foundations of hyperbolic manifolds (Springer-Verlag, New York, 1994). (Graduate Texts in Math.; 149). Google Scholar | DOI

[26] 26.De Rham, G., Reidemeister's torsion invariant and rotations of Sn, Differential analysis, Bombay Colloq. (Oxford University Press, London, 1964), 27–36. Google Scholar

[27] 27.Rothenberg, M., Torsion invariants and finite transformation groups, Proc. Symposia Pure Math. 32 (1978), 267–311. Google Scholar

[28] 28.Schlenker, J.-M., Dihedral angles of convex polyhedra, Discrete Comput. Geom. 23 (2000), 409–417. Google Scholar

[29] 29.Thurston, W. P., Geometry and topology of three-manifolds (Princeton University, 1979). (Princeton University Lecture Notes) Google Scholar

[30] 30.Vinberg, E. B., Editor, Geometry II. Spaces of constant curvature (Springer-Verlag, New York, 1993). (Encyclopaedia of Mathematical Sciences; 29) Google Scholar | DOI

[31] 31.Weiß, H., Local rigidity of 3-dimensional cone-manifolds, J. Diff. Geom. 71 (3) (2005), 437–506. Google Scholar

[32] 32.Weiß, H., Global rigidity of 3-dimensional cone-manifolds, J. Diff. Geom. 76 (3) (2007), 495–523. Google Scholar

[33] 33.Weiß, H., The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2π, Geom. Topol., arXiv:0904.4568. Google Scholar

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