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ON THE EFFICIENCY OF COXETER GROUPS

Published online by Cambridge University Press:  01 January 1997

Y. G. BAIK  and
S. J. PRIDE
Y. G. BAIK
Affiliation:
Department of Applied Mathematics, National Fisheries University of Pusan, Pusan 608-737, Republic of Korea
S. J. PRIDE
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, Scotland
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Abstract

If G is a finitely presented group and [Kscr ] is any (G,2)-complex (that is, a finite 2-complex with fundamental group G), then it is well known that χ([Kscr ]) [ges ] ν(G), where ν(G) = 1−rk H1G+dH2G. We define χ(G) to be min{χ([Kscr ]): [Kscr ] a (G, 2)-complex}, and we say that G is efficient if χ(G) = ν(G). In this paper we give sufficient conditions for a Coxeter group to be efficient (Theorem 4.2). We also give examples of inefficient Coxeter groups (Theorem 5.1). In fact, we give an infinite family Gn(n = 2, 3, 4, . . . ) of Coxeter groups such that χ(Gn)−ν(Gn) [xrarr ] ∞ as n [xrarr ] ∞.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 32 - 36
Copyright
© The London Mathematical Society 1997

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