Growth functions of Coxeter groups, Poincare series of singularities and $2$-tangle $q$-fractions

TL;DR

This paper explores the relationship between growth functions of Coxeter groups, Poincare series of certain singularities, and their representation as 2-tangle q-fractions, revealing new connections in geometric group theory and singularity theory.

Contribution

It establishes a novel link between Coxeter group growth functions, Poincare series, and 2-tangle q-fractions, advancing understanding of their algebraic and topological properties.

Findings

Growth functions of Coxeter groups are expressed as 2-tangle q-fractions.

Poincare series of Kleinian and Fuchsian singularities are represented as 2-tangle q-fractions.

The paper uncovers a unified framework connecting group growth, singularity invariants, and knot theory.

Abstract

Growth functions of Coxeter groups and the Poincare series of Kleinian and Fuchsian singularities are $2$-tangle $q$-fractions.