Journal of the Australian Mathematical Society  Series A
Vol. 64 Part 2 (1998)
Euler characteristics and imbeddings
of hyperbolic Coxeter groups
George Maxwell
Mathematics Department
University of British
Columbia
#1211984 Mathematics Road
Vancouver, B. C. V6T 1Y4
Canada
Abstract:
This paper has a twofold purpose. The first is to compute the Euler
characteristics of hyperbolic Coxeter groups W_{S} of level 1 or 2 by a
mixture of theoretical and computer aided methods. For groups of level 1
and odd values of S, the Euler characteristic is related to the volume
of the fundamental region of W_{S} in hyperbolic space. Secondly we note
two methods of imbedding such groups in each other. This reduces the
amount of computation needed to determine the Euler characteristics and
also reduces the number of essentially different hyperbolic groups that
need to be considered.
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