Geodesic
Spherical simplices generating discrete reflection groups
Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 585-598 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $P$ be a simplex in $\mathbb S^n$, and $G_P$ the group generated by reflections with respect to the faces of $P$. This paper considers the question of the conditions ensuring that $G_P$ is discrete. The main result is a description of all indecomposable spherical simplices generating discrete reflection groups. 
@article{SM_2004_195_4_a4,
     author = {A. A. Felikson},
     title = {Spherical simplices generating discrete reflection groups},
     journal = {Sbornik. Mathematics},
     pages = {585--598},
     year = {2004},
     volume = {195},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_4_a4/}
}
TY  - JOUR
AU  - A. A. Felikson
TI  - Spherical simplices generating discrete reflection groups
JO  - Sbornik. Mathematics
PY  - 2004
SP  - 585
EP  - 598
VL  - 195
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_2004_195_4_a4/
LA  - en
ID  - SM_2004_195_4_a4
ER  - 
%0 Journal Article
%A A. A. Felikson
%T Spherical simplices generating discrete reflection groups
%J Sbornik. Mathematics
%D 2004
%P 585-598
%V 195
%N 4
%U http://geodesic.mathdoc.fr/item/SM_2004_195_4_a4/
%G en
%F SM_2004_195_4_a4
A. A. Felikson. Spherical simplices generating discrete reflection groups. Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 585-598. http://geodesic.mathdoc.fr/item/SM_2004_195_4_a4/

[1] Schwarz H. A., “Über diejenige Fälle in welchen die Gaussische Reihe eine algeraische Function ihres elementes destellt”, Crelle's J., 75 (1873), 292–335

[2] Klimenko E., Sakuma M., “Two-generator discrete subgroups of $\operatorname{Isom}(H^2)$ containing orientation-reversing elements”, Geom. Dedicata, 72 (1998), 247–282 | DOI | MR | Zbl

[3] Felikson A., “Coxeter decompositions of hyperbolic polygons”, European J. Combin., 19 (1998), 801–817 | DOI | MR | Zbl

[4] Felikson A., Coxeter decompositions of hyperbolic pyramids and triangular prisms, Preprint No 00-006, Univ. of Bielefeld, Bielefeld, 2000; arXiv: math.MG/0212195

[5] Felikson A. A., “Koksterovskie razbieniya giperbolicheskikh simpleksov”, Matem. sb., 193:12 (2002), 134–156 ; arXiv: math.MG/0210067 | MR | Zbl

[6] Felikson A. A., “Kuby Lamberta, porozhdayuschie diskretnye gruppy otrazhenii”, Matem. zametki, 75:2 (2004), 277–286 | MR | Zbl

[7] Felikson A., Spherical simplices generating discrete reflection groups, Preprint, Univ. of Fribourg, Fribourg, 2002; arXiv: math.MG/0212244

[8] Coxeter H. S. M., “Discrete groups generated by reflections”, Ann. of Math. (2), 35:3 (1934), 588–621 | DOI | MR | Zbl

[9] Vinberg E. B., Shvartsman O. V., “Diskretnye gruppy dvizhenii prostranstv postoyannoi krivizny”, Itogi nauki i tekhniki. Sovrem. problemy matem. Fundament. napravleniya, 29, VINITI, M., 1988, 147–259

[10] Dynkin E. B., “Poluprostye podalgebry poluprostykh algebr Li”, Matem. sb., 30(72):2 (1952), 349–462 | MR | Zbl