Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0999.30028
Drumm, Todd A.; Poritz, Jonathan A.
Ford and Dirichlet domains for cyclic subgroups of $\text{PSL}_2({\Bbb C})$ acting on ${{\Bbb H}^3_{\Bbb R}}$ and ${\partial}{{\Bbb H}^3_{\Bbb R}}$. (English)
[J] Conform. Geom. Dyn. 3, No. 8, 116-150, electronic only (1999). ISSN 1088-4173/e

Summary: Let $\Gamma$ be a cyclic subgroup of $\text{PSL}_2({\Bbb C})$ generated by a loxodromic element. The Ford and Dirichlet fundamental domains for the action of $\Gamma$ on ${{\Bbb H}^3_{\Bbb R}}$ are the complements of configurations of half-balls centered on the plane at infinity ${\partial}{{\Bbb H}^3_{\Bbb R}}$. {\it T. Jørgensen} [Math. Scand. 33, 250-260 (1973; Zbl 0286.30017)] proved that the boundary of the intersection of the Ford fundamental domain with ${\partial}{{\Bbb H}^3_{\Bbb R}}$ always consists of either two, four, or six circular arcs and stated that an arbitrarily large number of hemispheres could contribute faces to the Ford domain in the interior of ${{\Bbb H}^3_{\Bbb R}}$. We give new proofs of Jørgensen's results, prove analogous facts for Dirichlet domains and for Ford and Dirichlet domains in the interior of ${{\Bbb H}^3_{\Bbb R}}$, and give a complete decomposition of the parameter space by the combinatorial type of the corresponding fundamental domain.

MSC 2000:: *30F40 Kleinian groups
20H10 Fuchsian groups and their generalizations (group theory)

Keywords: Ford domain; Dirichlet domain

Citations: Zbl 0286.30017

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]