Publication: Hyperbolic polygons and NEC groups
Loading...
Full text at PDC
Publication Date
1988
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Citations
Exportar
Abstract
Beardon gave a procedure for constructing a polygon with prescribed angles. For each ordered set of angles Beardon's polygon is unique up to congruence. The polygon obtained this way has an inscribed circle. It is possible to obtain by means of these polygons a fundamental region for a non-Euclidean crystallographic (NEC) group with a given signature having equal angles in each of the cycles. In [5] the minimal number of sides of a convex fundamental region of an NEC group is calculated, and regions are explicitly obtained achieving the bound.
Description
UCM subjects
Unesco subjects
Keywords
Citation
Beardon, A. F.. Hyperbolic polygons and Fuchsian groups. J. London Math. Soc. (2)20 (1979), 247–254.
Beardon, A. F.. The Geometry of Discrete Groups. Graduate Texts in Math. no. 91 (Springer-Verlag, 1983).
Macbeath, A. M.. The classification of non-Euclidean plane crystallographic groups. Canad. J. Math. 19 (1967), 1192–1205.
Macbeath, A. M. and Singerman, D.. Spaces of subgroups and Teichmüller space. Proc. London Math. Soc. (3) 31(1975), 211–256.
Martínez, E.. Convex fundamental regions for N.E.C. groups. Arch. Math. (Basel) 47 (1986), 457–464.
Singerman, P.. Symmetries of Riemann surfaces with large automorphism group. Math. Ann. 210 (1974), 17–32.
Singerman, D.. On the structure of non-Euclidean crystallographic groups. Proc. Cambridge Philos. Soc. 76 (1974), 233–240.
Wilkie, H. C.. On non-Euclidean crystallographic groups. Math. Z. 91(1966), 87–102.
Zieschang, H., Vogt, E. and Coldewey, H. D.. Surfaces and Planar Discontinuous Groups. Lecture Notes in Math. vol. 835 (Springer-Verlag, 1980).