EULER CHARACTERISTICS AND IMBEDDINGS OF HYPERBOLIC COXETER GROUPS

This paper has a twofold purpose. The first is to compute the Euler ch aracteristics of hyperbolic Coxeter groups Ws of level 1 or 2 by a mix ture of theoretical and computer aided methods. For groups of level 1 and odd values of \S\, the Euler characteristic is related to the volu me of the fundamental region of W-s in hyperbolic space. Secondly we n ote two methods of imbedding such groups in each other. This reduces t he amount of computation needed to determine the Euler characteristics and also reduces the number of essentially different hyperbolic group s that need to be considered.