In mathematics, a Bianchi group is a group of the form
where d is a positive square-free integer. Here, PSL denotes the projective special linear group and Od is the ring of integers of the imaginary quadratic field Q(√−d).
The groups were first studied by Bianchi (1892) as a natural class of discrete subgroups of PSL2(C), now termed Kleinian groups.
As a subgroup of PSL2(C), a Bianchi group acts as orientation-preserving isometries of 3-dimensional hyperbolic space H3. The quotient space Md = PSL2(Od) \ H3 is a non-compact, hyperbolic 3-fold with finite volume. An exact formula for the volume, in terms of the Dedekind zeta function of the base field Q(√−d), was computed by Humbert. The set of cusps of Md is in bijection with the class group of Q(√−d). It is well-known that any non-cocompact arithmetic Kleinian group is weakly commensurable with a Bianchi group.
- ^ Maclachlan & Reid (2003) p.58
- Bianchi, Luigi (1892), "Sui gruppi di sostituzioni lineari con coefficienti appartenenti a corpi quadratici immaginarî", Mathematische Annalen (Springer Berlin / Heidelberg) 40: 332–412, doi:10.1007/BF01443558, ISSN 0025-5831
- Elstrodt, Juergen; Grunewald, Fritz; Mennicke, Jens (1998). Groups Acting On Hyperbolic Spaces. Springer Monographs in Mathematics. Springer. ISBN 3-540-62745-6.
- Fine, Benjamin (1989), Algebraic theory of the Bianchi groups, Monographs and Textbooks in Pure and Applied Mathematics 129, New York: Marcel Dekker Inc., ISBN 978-0-8247-8192-7, MR 1010229
- Fine, B. (2001), "Bianchi group", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Maclachlan, Colin; Reid, Alan W. (2003). The Arithmetic of Hyperbolic 3-Manifolds. Graduate Texts in Mathematics 219. Springer-Verlag. ISBN 0-387-98386-4. Zbl 1025.57001.
Times of Malta
Sun, 08 Dec 2013 23:52:30 -0800
... BC Hamburg from Sfax to Misurata (all Thomas Smith Shipping Ltd), the MV Eurocargo Malta from Genoa to Livorno, the MV Euroferry Malta from Salerno to Salerno (both Sullivan Maritime) and the Primavera from Valencia to Livorno (Bianchi Group) today.
Thu, 28 Nov 2013 00:37:17 -0800
The other partners in the consortium are Vienna International Airport with 53.24%, and the Bianchi Group, with 10.63%. In August, MaltaToday reported that the Canadian company could pull out of MIA after the company made a surprise disclosure of a ...
Mon, 25 Nov 2013 06:51:24 -0800
The Canadian engineers own 36.13% of the private, 40% shareholding of MIA that is owned by the Malta Mediterranean Link consortium: the other partners are Vienna International Airport with 53.24%, and the Bianchi Group, with 10.63%. The company ...
ADV Express (Abbonamento)
ADV Express (Abbonamento)
Fri, 06 Dec 2013 09:15:00 -0800
Alessia Bianchi Group conclude l'anno con l'acquisizione di un nuovo importante cliente: Value Collection, società specializzata nella compravendita di orologi e oggetti da collezione. L'agenzia comasca avrà il compito di gestire l'ufficio stampa ...
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