Euler characteristics and imbeddings
of hyperbolic Coxeter groups

George Maxwell
Mathematics Department
University of British Columbia
#121-1984 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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