Euler characteristics for one-relator products of groups

Williams, Gerald (2007) Euler characteristics for one-relator products of groups. Bulletin of the London Mathematical Society, 39 (4). pp. 641-652. ISSN 0024-6093. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1112/blms/bdm052

Abstract

We calculate Euler characteristics for one-relator products of groups G = (G(1) * G(2))IN(R-m) under certain conditions on the form of R and the value of m. As special cases, we study one-relator products of cyclics and recover and generalize results of Fine, Rosenberger and Stille. As corollaries to our main results, we give a necessary condition for G to admit a faithful, discrete representation to PSL(2,C) of finite covolume. In particular, we generalize a result of Hagelberg, Maclachlan and Rosenberger, from the context of generalized triangle groups to that of one-relator products induced by generalized triangle groups. This provides an answer to a question of Fine and Rosenberger. In deriving our Euler characteristic results we study relators R-m with a 'multiply exceptional form', and establish a connection with a class of orbifolds studied by Jones and Reid.

Item Type: Article
Uncontrolled keywords: GENERALIZED TRIANGLE GROUPS; HIGH-POWERED RELATOR; DISCRETE GROUPS; COXETER GROUPS; SUBGROUPS; QUOTIENT; CYCLICS
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Judith Broom
Date Deposited: 07 Jul 2008 09:25
Last Modified: 14 Jan 2010 14:40
Resource URI: https://kar.kent.ac.uk/id/eprint/10475 (The current URI for this page, for reference purposes)
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