Title:
|
On the boundary of 2-dimensional ideal polyhedra (English) |
Author:
|
Vrontakis, Emmanuel |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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47 |
Issue:
|
2 |
Year:
|
2006 |
Pages:
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359-367 |
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Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
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CAT$(-1)$ spaces |
Keyword:
|
ideal polyhedron |
Keyword:
|
visual boundary |
MSC:
|
53C23 |
MSC:
|
57M20 |
idZBL:
|
Zbl 1150.57301 |
idMR:
|
MR2241537 |
. |
Date available:
|
2009-05-05T16:57:51Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119597 |
. |
Reference:
|
[1] Benakli N.: Polyédres hyperboliques, passage du local au global.Thése, Université de Paris-Sud, 1992. |
Reference:
|
[2] Bourdon M.: Structure conforme au bord et flot géodésique d'un CAT$(-1)$-espace.Enseign. Math. 41 (1995), 63-102. MR 1341941 |
Reference:
|
[3] Coornaert M.: Sur les groupes proprement discontinus d'isometries des espaces hyperboliques au sens de Gromov.Thèse, U.L.P., 1990. Zbl 0777.53044 |
Reference:
|
[4] Charitos C., Papadopoulos A.: The geometry of ideal $2$-dimensional simplicial complexes.Glasgow Math. J. 43 39-66 (2001). Zbl 0977.57003, MR 1825722 |
Reference:
|
[5] Charitos C., Papadopoulos A.: Hyperbolic structures and measured foliations on $2$-dimensional complexes.Monatsh. Math. 139 1-17 (2003). Zbl 1029.57003, MR 1981114 |
Reference:
|
[6] Charitos C., Papadopoulos A.: On the isometries of ideal polyhedra.Rend. Circ. Mat. Palermo (2) 54 1 (2005), 71-80. Zbl 1194.57006, MR 2150807 |
Reference:
|
[7] Charitos C., Tsapogas G.: Geodesic flow on ideal polyhedra.Canad. J. Math. 49 4 696-707 (1997). Zbl 0904.52004, MR 1471051 |
Reference:
|
[8] Charitos C., Tsapogas G.: Complexity of geodesics on $2$-dimensional ideal polyhedra and isotopies.Math. Proc. Camb. Phil. Soc. 121 343-358 (1997). Zbl 0890.57047, MR 1426528 |
Reference:
|
[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. Zbl 0731.20025, MR 1086648 |
Reference:
|
[10] Gromov M.: Structures Métriques pour les Variétés Riemanniennes.J. Lafontaine and P. Pansu, Eds., Fernand Nathan, Paris, 1981. Zbl 0509.53034, MR 0682063 |
Reference:
|
[11] Gromov M.: Hyperbolic Groups.in Essays in Group Theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp.75-263. Zbl 1022.20501, MR 0919829 |
Reference:
|
[12] Haglund F.: Les polyédres de Gromov.Thése, Université de Lyon I, 1992. Zbl 0749.52011, MR 1133493 |
Reference:
|
[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. Zbl 1044.20028, MR 1921706 |
Reference:
|
[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. Zbl 0843.20032, MR 1170371 |
Reference:
|
[15] Thurston W.P.: Three-dimensional Geometry and Topology.Princeton University Press, Princeton, NJ, 1997. Zbl 0873.57001, MR 1435975 |
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