Bipolar Coxeter groups

Details Bipolar Coxeter groups Bipolar Coxeter groups

2010-02-21

arxiv.org/abs/1002.3991v1

J. Algebra 338 Nr. 1 (2011) pp. 35--55

Mathematics

Group Theory

25 pages, 2 figures

Scientific paper

10.1016/j.jalgebra.2011.05.007

We consider the class of those Coxeter groups for which removing from the Cayley graph any tubular neighbourhood of any wall leaves exactly two connected components. We call these Coxeter groups bipolar. They include both the virtually Poincare duality Coxeter groups and the infinite irreducible 2-spherical ones. We show in a geometric way that a bipolar Coxeter group admits a unique conjugacy class of Coxeter generating sets. Moreover, we provide a characterisation of bipolar Coxeter groups in terms of the associated Coxeter diagram.

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