Faculté des sciences

The growth function of Coxeter garlands in $\mathbb{H}^4$

Zehrt, Thomas ; Zehrt-Liebendörfer, Christine

In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2012, p. -

The growth function W(t) of a Coxeter group W relative to a Coxeter generating set is always a rational function. We prove by an explicit construction that there are infinitely many cocompact Coxeter groups W in hyperbolic 4-space with the following property. All the roots of the denominator of W(t) are on the unit circle except exactly two pairs of real roots. Plus

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    Summary
    The growth function W(t) of a Coxeter group W relative to a Coxeter generating set is always a rational function. We prove by an explicit construction that there are infinitely many cocompact Coxeter groups W in hyperbolic 4-space with the following property. All the roots of the denominator of W(t) are on the unit circle except exactly two pairs of real roots.