Geodesic
The three smallest compact arithmetic hyperbolic 5–orbifolds
Emery, Vincent1 ; Kellerhals, Ruth2
1Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany
2Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 817-829
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We determine the three hyperbolic 5–orbifolds of smallest volume among compact arithmetic orbifolds, and we identify their fundamental groups with hyperbolic Coxeter groups.

DOI : 10.2140/agt.2013.13.817
Classification : 22E40, 11R42, 20F55, 51M25
Keywords: hyperbolic orbifolds, hyperbolic volume, arithmetic groups, Coxeter groups

Emery, Vincent  1   ; Kellerhals, Ruth  2

1 Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany
2 Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland 
@article{10_2140_agt_2013_13_817,
     author = {Emery, Vincent and Kellerhals, Ruth},
     title = {The three smallest compact arithmetic hyperbolic 5{\textendash}orbifolds},
     journal = {Algebraic and Geometric Topology},
     pages = {817--829},
     year = {2013},
     volume = {13},
     number = {2},
     doi = {10.2140/agt.2013.13.817},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.817/}
}
TY  - JOUR
AU  - Emery, Vincent
AU  - Kellerhals, Ruth
TI  - The three smallest compact arithmetic hyperbolic 5–orbifolds
JO  - Algebraic and Geometric Topology
PY  - 2013
SP  - 817
EP  - 829
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.817/
DO  - 10.2140/agt.2013.13.817
ID  - 10_2140_agt_2013_13_817
ER  - 
%0 Journal Article
%A Emery, Vincent
%A Kellerhals, Ruth
%T The three smallest compact arithmetic hyperbolic 5–orbifolds
%J Algebraic and Geometric Topology
%D 2013
%P 817-829
%V 13
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.817/
%R 10.2140/agt.2013.13.817
%F 10_2140_agt_2013_13_817
Emery, Vincent; Kellerhals, Ruth. The three smallest compact arithmetic hyperbolic 5–orbifolds. Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 817-829. doi: 10.2140/agt.2013.13.817

[1] M Belolipetsky, V Emery, On volumes of arithmetic quotients of $\mathrm{PO}(n,1)^\circ$, $n$ odd, Proc. Lond. Math. Soc. 105 (2012) 541

[2] , The Bordeaux database

[3] V O Bugaenko, Groups of automorphisms of unimodular hyperbolic quadratic forms over the ring $\mathbf{Z}[(\sqrt{5}+1)/2]$, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1984) 6

[4] H Cohen, F Diaz Y Diaz, M Olivier, Computing ray class groups, conductors and discriminants, Math. Comp. 67 (1998) 773

[5] V Emery, Du volume des quotients arithmétiques de l'espace hyperbolique, PhD thesis, University of Fribourg (2009)

[6] S Freundt, QaoS online database

[7] H C Im Hof, Napier cycles and hyperbolic Coxeter groups, Bull. Soc. Math. Belg. Sér. A 42 (1990) 523

[8] R Kellerhals, Scissors congruence, the golden ratio and volumes in hyperbolic $5$–space, Discrete Comput. Geom. 47 (2012) 629

[9] H Klingen, Über die Werte der Dedekindschen Zetafunktion, Math. Ann. 145 (1961/1962) 265

[10] V S Makarov, The Fedorov groups of four-dimensional and five-dimensional Lobačevskiĭspace, from: "Studies in General Algebra", Kišinev. Gos. Univ., Kishinev (1968) 120

[11] J Milnor, The Schläfli differential equality, from: "Collected papers", Publish or Perish (1994)

[12] A Mohammadi, A Salehi Golsefidy, Discrete subgroups acting transitively on vertices of a Bruhat–Tits building, Duke Math. J. 161 (2012) 483

[13] G Prasad, Volumes of $S$–arithmetic quotients of semi-simple groups, Inst. Hautes Études Sci. Publ. Math. (1989) 91

[14] È B Vinberg, Discrete groups generated by reflections in Lobačevskiĭ spaces, Math. USSR Sb. 1 (1967) 429

[15] D Zagier, H Gangl, Classical and elliptic polylogarithms and special values of $L$–series, from: "The arithmetic and geometry of algebraic cycles" (editors B B Gordon, J D Lewis, S Müller-Stach, S Saito, N Yui), NATO Sci. Ser. C Math. Phys. Sci. 548, Kluwer Acad. Publ. (2000) 561

Cité par Sources :