Essential hyperbolic Coxeter polytopes

Felikson, A.; Tumarkin, P.

doi:10.1007/s11856-013-0046-3

Essential hyperbolic Coxeter polytopes

Felikson, A.; Tumarkin, P.

Authors

Professor Anna Felikson anna.felikson@durham.ac.uk
Professor

Professor Pavel Tumarkin pavel.tumarkin@durham.ac.uk
Professor

Abstract

We introduce a notion of an essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimension at least 6 which are known to be essential, and prove that this class contains finitely many polytopes only. We also construct an effective algorithm of classifying polytopes from this class, realize it in the four-dimensional case, and formulate a conjecture on finiteness of the number of essential polytopes.

Citation

Felikson, A., & Tumarkin, P. (2014). Essential hyperbolic Coxeter polytopes. Israel Journal of Mathematics, 199(1), 113-161. https://doi.org/10.1007/s11856-013-0046-3

Journal Article Type	Article
Online Publication Date	Oct 10, 2013
Publication Date	Jan 1, 2014
Deposit Date	Mar 19, 2012
Publicly Available Date	Mar 19, 2014
Journal	Israel Journal of Mathematics
Print ISSN	0021-2172
Electronic ISSN	1565-8511
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	199
Issue	1
Pages	113-161
DOI	https://doi.org/10.1007/s11856-013-0046-3