On -dimensional compact hyperbolic Coxeter polytopes with
facets
Authors:
Pavel Tumarkin and Anna Felikson
Translated by:
Alex Martsinkovsky
Original publication:
Trudy Moskovskogo Matematicheskogo Obshchestva, tom 69 (2008).
Journal:
Trans. Moscow Math. Soc. 2008, 105-151
MSC (2000):
Primary 52B11; Secondary 20F55
DOI:
https://doi.org/10.1090/S0077-1554-08-00172-6
Published electronically:
November 20, 2008
MathSciNet review:
2549446
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that there are no compact Coxeter polytopes with facets in a hyperbolic space of dimension
. This estimate is sharp: examples of such polytopes in dimensions
were found by V. O. Bugaenko in 1984. We also show that in dimension
there is a unique polytope with 11 facets.
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Additional Information
Pavel Tumarkin
Affiliation:
Independent University of Moscow, Russia
Email:
pasha@mccme.ru
Anna Felikson
Affiliation:
Independent University of Moscow, Russia
Email:
felikson@mccme.ru
DOI:
https://doi.org/10.1090/S0077-1554-08-00172-6
Published electronically:
November 20, 2008
Additional Notes:
The first author was partially supported by the President of the Russian Federation grants MK-6290.2006.1 and NSh-5666.2006.1, the RFFI grant No. 07-01-00390-a, and the INTAS grant YSF-06-10000014-5766.
The second author was partially supported by the President of the Russian Federation grant NSh-5666.2006.1, the RFFI grant No. 07-01-00390-a, and the INTAS grant YSF-06-10000014-5916.
Article copyright:
© Copyright 2008
American Mathematical Society