Ford and Dirichlet domains for cyclic subgroups of acting on and
Authors:
Todd A. Drumm and Jonathan A. Poritz
Journal:
Conform. Geom. Dyn. 3 (1999), 116150
MSC (1991):
Primary 20H10; Secondary 57M60, 57S30, 57S25
Published electronically:
October 25, 1999
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MathSciNet review:
1716572
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Abstract: Let be a cyclic subgroup of generated by a loxodromic element. The Ford and Dirichlet fundamental domains for the action of on are the complements of configurations of halfballs centered on the plane at infinity . Jørgensen (On cyclic groups of Möbius transformations, Math. Scand. 33 (1973), 250260) proved that the boundary of the intersection of the Ford fundamental domain with 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 . We give new proofs of Jørgensen's results, prove analogous facts for Dirichlet domains and for Ford and Dirichlet domains in the interior of , and give a complete decomposition of the parameter space by the combinatorial type of the corresponding fundamental domain.
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(85d:22026)
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Jørgensen, On cyclic groups of Möbius
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 A. Beardon, The geometry of discrete groups, SpringerVerlag, New York, 1983. MR 85d:22026
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Additional Information
Todd A. Drumm
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA 19081
Email:
tad@swarthmore.edu
Jonathan A. Poritz
Affiliation:
Department of Mathematics, Georgetown University, Washington, DC 20057
Email:
poritz@math.georgetown.edu
DOI:
http://dx.doi.org/10.1090/S1088417399000429
PII:
S 10884173(99)000429
Keywords:
Fundamental domain,
Ford domain,
Dirichlet domain,
hyperbolic geometry
Published electronically:
October 25, 1999
Additional Notes:
The first author was partially supported by the Swarthmore College Research Fund.
The second author was partially supported by NSF grant DMS9403784.
Article copyright:
© Copyright 1999
American Mathematical Society
