On the boundary of 2-dimensional ideal polyhedra

Emmanuel Vrontakis

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 2, page 359-367
  • ISSN: 0010-2628

Abstract

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It is proved that for every two points in the visual boundary of the universal covering of a 2 -dimensional ideal polyhedron, there is an infinity of paths joining them.

How to cite

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Vrontakis, Emmanuel. "On the boundary of 2-dimensional ideal polyhedra." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 359-367. <http://eudml.org/doc/249880>.

@article{Vrontakis2006,
abstract = {It is proved that for every two points in the visual boundary of the universal covering of a $2$-dimensional ideal polyhedron, there is an infinity of paths joining them.},
author = {Vrontakis, Emmanuel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {CAT$(-1)$ spaces; ideal polyhedron; visual boundary; CAT spaces; ideal polyhedron; visual boundary},
language = {eng},
number = {2},
pages = {359-367},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the boundary of 2-dimensional ideal polyhedra},
url = {http://eudml.org/doc/249880},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Vrontakis, Emmanuel
TI - On the boundary of 2-dimensional ideal polyhedra
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 2
SP - 359
EP - 367
AB - It is proved that for every two points in the visual boundary of the universal covering of a $2$-dimensional ideal polyhedron, there is an infinity of paths joining them.
LA - eng
KW - CAT$(-1)$ spaces; ideal polyhedron; visual boundary; CAT spaces; ideal polyhedron; visual boundary
UR - http://eudml.org/doc/249880
ER -

References

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  1. Benakli N., Polyédres hyperboliques, passage du local au global, Thése, Université de Paris-Sud, 1992. 
  2. Bourdon M., Structure conforme au bord et flot géodésique d’un CAT ( - 1 ) -espace, Enseign. Math. 41 (1995), 63-102. (1995) MR1341941
  3. Coornaert M., Sur les groupes proprement discontinus d'isometries des espaces hyperboliques au sens de Gromov, Thèse, U.L.P., 1990. Zbl0777.53044
  4. Charitos C., Papadopoulos A., The geometry of ideal 2 -dimensional simplicial complexes, Glasgow Math. J. 43 39-66 (2001). (2001) Zbl0977.57003MR1825722
  5. Charitos C., Papadopoulos A., Hyperbolic structures and measured foliations on 2 -dimensional complexes, Monatsh. Math. 139 1-17 (2003). (2003) Zbl1029.57003MR1981114
  6. Charitos C., Papadopoulos A., On the isometries of ideal polyhedra, Rend. Circ. Mat. Palermo (2) 54 1 (2005), 71-80. (2005) Zbl1194.57006MR2150807
  7. Charitos C., Tsapogas G., Geodesic flow on ideal polyhedra, Canad. J. Math. 49 4 696-707 (1997). (1997) Zbl0904.52004MR1471051
  8. Charitos C., Tsapogas G., Complexity of geodesics on 2 -dimensional ideal polyhedra and isotopies, Math. Proc. Camb. Phil. Soc. 121 343-358 (1997). (1997) Zbl0890.57047MR1426528
  9. Ghys E., de la Harpe P., Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics, vol. 83, Birkhäuser, Boston, 1990, pp.1-25. Zbl0731.20025MR1086648
  10. Gromov M., Structures Métriques pour les Variétés Riemanniennes, J. Lafontaine and P. Pansu, Eds., Fernand Nathan, Paris, 1981. Zbl0509.53034MR0682063
  11. Gromov M., Hyperbolic Groups, in Essays in Group Theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp.75-263. Zbl1022.20501MR0919829
  12. Haglund F., Les polyédres de Gromov, Thése, Université de Lyon I, 1992. Zbl0749.52011MR1133493
  13. Kapovich I., Benakli N., Boundaries of hyperbolic groups, Combinatorial and Geometric Group Theory (New York, 2000/Hoboken, NJ, 2001), Contemp. Math. 296, Amer. Math. Soc., Providence, RI, 2002, pp.39-93. Zbl1044.20028MR1921706
  14. Paulin F., Constructions of hyperbolic groups via hyperbolizations of polyhedra, in: Group Theory from a Geometrical Viewpoint, ICTP, Trieste, Italy, 1990, E. Ghys and A. Haefliger, Eds., World Sci. Publishing, River Edge, NJ, 1991, pp.313-372. Zbl0843.20032MR1170371
  15. Thurston W.P., Three-dimensional Geometry and Topology, Princeton University Press, Princeton, NJ, 1997. Zbl0873.57001MR1435975

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